equation_gpt_train_economics.jsonl

{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level is: Marginal Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The Latex Code for equation Sharpe Ratiois <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Sharpe Ratio?"}
{"completion": " The related materials of Consumer Price Index CPI is: 1.Investopedia: Consumer Price Index:<url>https://www.investopedia.com/terms/c/consumerpriceindex.asp</url>;2.CPI Home : U.S. Bureau of Labor Statistics:<url>https://www.bls.gov/cpi/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Consumer Price Index CPI?"}
{"completion": " The Latex Code for equation Marginal Revenueis <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Marginal Revenue?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand is: Percentage change in Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue is: Change in Quantity(Q).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{Q}</equation> in Marginal Revenue?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>AVC</equation> in Average Variable Cost is: Average Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>AVC</equation> in Average Variable Cost?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSC</equation> in Allocative Efficiency Condition is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MSC</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output?"}
{"completion": " The Latex Code for equation Forwardsis <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Forwards?"}
{"completion": " The Latex Code for equation Effective Rateis <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>", "tag": "Economics", "prompt": "How to write equation Effective Rate?"}
{"completion": " The equation for Price for a Competitive Firm is: <equation>P = MR</equation>. Here is the brief introduction of Price for a Competitive Firm:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal revenue (MR)\n: Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Price for a Competitive Firm?"}
{"completion": " The Latex Code for equation Equation of Exchangeis <equation>\\\\text{MV} = \\\\text{PQ}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Equation of Exchange?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options is: put protection if the stock price should fall..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>p(S_{t}, K)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Average Variable Cost is: <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Variable Cost:\n        Latex code for the Average Variable Cost. I will briefly introduce the notations in this formulation.  \n        \n: Average Variable Cost\n: Total Variable Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Average Variable Cost?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve is: Change in Total Product.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve?"}
{"completion": " The Latex Code for equation Put-Call Parityis <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Put-Call Parity?"}
{"completion": " The Latex Code for equation Risk-Neutral Valuation and Power Contractsis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The Latex Code for equation Cox-Ingersoll-Ross CIRis <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>A(T)</equation> in Asian Options is: Arithmetic average of option price at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>A(T)</equation> in Asian Options?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MR</equation> in Marginal Revenue?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>n</equation> in Present Value of Ordinary Annuities is: Total number of times compounded, n=mt.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>n</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MRP</equation> in Factor of Production Hiring Rule is: Marginal revenue product.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MRP</equation> in Factor of Production Hiring Rule?"}
{"completion": " The Latex Code for equation Nominal Interest Rateis <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Nominal Interest Rate?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is: <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. Here is the brief introduction of Geometric Brownian Motion SDEs:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>i</equation> in Present Value of Ordinary Annuities is: Rate per period, usually i=r/m.", "tag": "Economics", "prompt": "What does the symbol mean <equation>i</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Profit is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{TC}</equation> in Profit?"}
{"completion": " The Latex Code for equation Slope of the Total Product Curveis <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Slope of the Total Product Curve?"}
{"completion": " The equation for Forwards is: <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. Here is the brief introduction of Forwards:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. A forward contract is an agreement in which the buyer agrees at time t to pay the seller at time T and receive the asset at time T.\n        \n: Forward Contract at strike price S\n: Interest Rate\n: Future Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Forwards?"}
{"completion": " The related materials of Allocative Efficiency Condition is: 1.Allocative Efficiency: Definition, Example Productive Efficiency:<url>https://boycewire.com/what-is-allocative-efficiency</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Allocative Efficiency Condition?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor is: Change in Total Product(TP).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts is: Price of the power contract.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I</equation> in Investment is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>I</equation> in Investment?"}
{"completion": " The equation for Marginal Factor Cost MFC is: <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. Here is the brief introduction of Marginal Factor Cost MFC:\n        Latex code for Marginal Revenue Product of Labor MRPL. Marginal factor cost (MFC) is the change in total cost (\\Delta \\text{TC}}) divided by the change in the quantity of the factor:\n        \n: Marginal Factor Cost\n: Change in total cost\n: Change in the quantity of the factor\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Marginal Factor Cost MFC?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>QI</equation> in Average Product is: Quantity of Input.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>QI</equation> in Average Product?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts is: Payoff a power contract at time T.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Optimal Combination of Resources Condition is: Price.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The Latex Code for equation Slope of the Total Product Curveis <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Slope of the Total Product Curve?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: Pay the strike earlier and therefore miss the interest on that money.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost is: Change in Quantity.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{Q}</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Merchandise Trade Balanceis <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Merchandise Trade Balance?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Effective Rate is: <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. Here is the brief introduction of Effective Rate:\n        Latex code for the Effective Rate. I will briefly introduce the notations in this formulation. \n        \n: Effective Rate\n: Compute the effective rate if your loan/investment is compounded m times per year.\n: Compute the effective rate if your loan/investment is compounded continuously.\n\n\nRelated Documents\n\nInvestopedia Effective Rate\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Please give me detailed tutorial of Effective Rate?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>n</equation> in Present Value of Ordinary Annuities is: Total number of times compounded, n=mt.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>n</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Marginal Revenue is: <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Revenue:\n        Latex code for Marginal Revenue. \n        \n: Marginal Revenue\n: Change in Total Revenue(TR)\n: Change in Quantity(Q)\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Marginal Revenue?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>Y(t)</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition is: Marginal Utility of C.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MU_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>MPL</equation> in Marginal Product of Labor is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MPL</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Profit-Maximizing Output Levelis <equation>MR = MC</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Profit-Maximizing Output Level?"}
{"completion": " The Latex Code for equation Present Value of Ordinary Annuitiesis <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>", "tag": "Economics", "prompt": "What is the equation of Present Value of Ordinary Annuities?"}
{"completion": " The equation for Production Efficiency Condition is: <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. Here is the brief introduction of Production Efficiency Condition:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal Product Label\n\n\nRelated Documents\n\nProduction Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Production Efficiency Condition?"}
{"completion": " The related materials of Production Efficiency Condition is: 1.Production Efficiency:<url>https://www.investopedia.com/terms/p/production_efficiency.asp</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Production Efficiency Condition?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve is: Total Product Curve.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Factor of Production Hiring Rule is: <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. Here is the brief introduction of Factor of Production Hiring Rule:\n        Latex code for Factor of Production Hiring Rule. I will briefly introduce the notations in this formulation.  \n        \n: Marginal revenue product\n: Marginal factor cost (MFC)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Factor of Production Hiring Rule?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC is: Marginal Factor Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Average Revenue is: <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>. Here is the brief introduction of Average Revenue:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Average Revenue?"}
{"completion": " The Latex Code for equation Consumption Functionis <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Consumption Function?"}
{"completion": " The related materials of Cox-Ingersoll-Ross CIR is: 1.A THEORY OF THE TERM STRUCTURE OF INTEREST RATES:<url>https://pages.stern.nyu.edu/~dbackus/BCZ/discrete_time/CIR_Econometrica_85.pdf</url>;2.Cox-Ingersoll-Ross (CIR) model-Mathworks:<url>https://www.mathworks.com/help/finance/cir.html</url>;3.Cox-Ingersoll-Ross Model:<url>https://www.investopedia.com/terms/c/cox-ingersoll-ross-model.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>R</equation> in Present Value of Ordinary Annuities is: Payment made in each period.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>R</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Consumption Function is: <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>. Here is the brief introduction of Consumption Function:\n        Latex code for Consumption Function.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Consumption Function?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio is: Sharpe ratio of any asset written on a GBM.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio?"}
{"completion": " The Latex Code for equation Marginal Revenue Productis <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Marginal Revenue Product?"}
{"completion": " The Latex Code for equation Effective Rateis <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>", "tag": "Economics", "prompt": "Show me the latex code of equation Effective Rate?"}
{"completion": " The equation for Simple Interest is: <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. Here is the brief introduction of Simple Interest:\n        Latex code for the Simple Interest. I will briefly introduce the notations in this formulation. \n        \n: Interest Earned\n: Principal/Present Value\n: Annual Rate\n: Time (years)\n: Future Value/Maturity Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you explain Simple Interest?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections is: Exports.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Future Value of Ordinary Annuities is: <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. Here is the brief introduction of Future Value of Ordinary Annuities:\n        Latex code for the Future Value of Ordinary Annuities. The payment/deposit is at the END of the period. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Please give me detailed tutorial of Future Value of Ordinary Annuities?"}
{"completion": " The equation for Optimal Combination of Resources Condition is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Optimal Combination of Resources Condition:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>A</equation> in Simple Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "What does the symbol mean <equation>A</equation> in Simple Interest?"}
{"completion": " The equation for Consumption Function is: <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>. Here is the brief introduction of Consumption Function:\n        Latex code for Consumption Function.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Consumption Function?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>R</equation> in Annuities Due is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "What is the meaning of <equation>R</equation> in Annuities Due?"}
{"completion": " The equation for Consumption Function is: <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>. Here is the brief introduction of Consumption Function:\n        Latex code for Consumption Function.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Consumption Function?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections is: Government Spending.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Calls and Puts Arbitrage is: <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. Here is the brief introduction of Calls and Puts Arbitrage:\n\n        Latex code for the Calls and Puts Arbitrage. Three different options have strike prices K1, K2, K3 and K1 < K2 < K3 holds.\n        An important formula for determining arbitrage opportunities comes from the following equations.\n        \n\n: Strike price of option 1\n: Strike price of option 2\n: Strike price of option 3\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Calls and Puts Arbitrage?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue is: Change in Quantity(Q).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is: <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. Here is the brief introduction of Geometric Brownian Motion SDEs:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections is: Government Spending.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>\\text{G}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand is: Percentage change in Price.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs is: Volatility.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>MU</equation> in Optimal Consumption Rule is: Marginal utility (MU).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MU</equation> in Optimal Consumption Rule?"}
{"completion": " The Latex Code for equation Ito Lemmais <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Ito Lemma?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations is: The variance of stock price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>AVC</equation> in Average Variable Cost is: Average Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>AVC</equation> in Average Variable Cost?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{A}</equation> in Gini Coefficient is: Area between Line of Perfect Equality and Lorenz Curve..", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>S_{A}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Annuities Dueis <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>", "tag": "Economics", "prompt": "Please give me some hints on equation Annuities Due?"}
{"completion": " The Latex Code for equation Real Interest Rateis <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Real Interest Rate?"}
{"completion": " The equation for Annuities Due is: <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. Here is the brief introduction of Annuities Due:\n        Latex code for the Future Value of Annuities Due. I will briefly introduce the notations in this formulation. \n        The payment/deposit is at the BEGINNING of the period\n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "What's the meaning of Annuities Due?"}
{"completion": " The Latex Code for equation Allocative Efficiency Conditionis <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Allocative Efficiency Condition?"}
{"completion": " The equation for Marginal Product of Labor is: <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. Here is the brief introduction of Marginal Product of Labor:\n        Latex code for Marginal Product of Labor. \n        \n: Marginal Product of Labor\n: Change in Total Product(TP)\n: Change in Labor(L)\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Marginal Product of Labor?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>r</equation> in Simple Interest is: Annual Rate.", "tag": "Economics", "prompt": "What is the meaning of <equation>r</equation> in Simple Interest?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts is: Price of the power contract.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The Latex Code for equation Marginal Revenueis <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Marginal Revenue?"}
{"completion": " The Latex Code for equation Marginal Revenue Product of Labor MRPLis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Real GDPis <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Real GDP?"}
{"completion": " The equation for Production Efficiency Condition is <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. The meaning of symbol <equation>MP_{L}</equation> in Production Efficiency Condition is: Marginal Product Label.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MP_{L}</equation> in Production Efficiency Condition?"}
{"completion": " The related materials of Standard Brownian Motion is: 1.Investopedia Simple Interest:<url>https://www.investopedia.com/terms/s/simple_interest.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Standard Brownian Motion?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSC</equation> in Allocative Efficiency Condition is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MSC</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts is: Risk-neutral equations.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Marginal Product of Laboris <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Marginal Product of Labor?"}
{"completion": " The related materials of Profit-Maximizing Output Level is: 1.Profit:<url>https://www.investopedia.com/terms/p/profit.asp</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Profit-Maximizing Output Level?"}
{"completion": " The Latex Code for equation Marginal Product of Laboris <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Marginal Product of Labor?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>FV</equation> in Forwards is: Future Value.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>FV</equation> in Forwards?"}
{"completion": " The Latex Code for equation Call and Put Price Boundsis <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Call and Put Price Bounds?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>t</equation> in Simple Interest is: Time (years).", "tag": "Economics", "prompt": "Can you explain the symbol <equation>t</equation> in Simple Interest?"}
{"completion": " The Latex Code for equation Cross-Price Elasticity of Demandis <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Standard Brownian Motionis <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Standard Brownian Motion?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>G(T)</equation> in Asian Options is: Geometric average of option price at time T.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>G(T)</equation> in Asian Options?"}
{"completion": " The Latex Code for equation Price for a Competitive Firmis <equation>P = MR</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Price for a Competitive Firm?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\sigma</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations is: The variance of stock price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Distributive Efficiency Condition is: <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. Here is the brief introduction of Distributive Efficiency Condition:\n        Latex code for Distributive Efficiency Condition. I will briefly introduce the notations in this formulation. Distributive efficiency is concerned with an equitable distribution of resources because of the law of diminishing marginal returns. The Law of diminishing marginal returns states that as consumption of a good increase we tend to get diminishing marginal utility. \n        \n: Marginal Utility of F\n: Product of F\n: Marginal Utility of C\n: Product of C\n\n\nRelated Documents\n\nDistributive Efficiency Definition\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Distributive Efficiency Condition?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC is: Change in total cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Equality of Leakages and Injections is: <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. Here is the brief introduction of Equality of Leakages and Injections:\n        Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy \u00e2\u20ac\u201c that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.\n        \n: Investment\n: Government Spending\n: Exports\n\n\nRelated Documents\n\nWhy are leakages equal to injections?\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Equality of Leakages and Injections?"}
{"completion": " The equation for Production Efficiency Condition is: <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. Here is the brief introduction of Production Efficiency Condition:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal Product Label\n\n\nRelated Documents\n\nProduction Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Production Efficiency Condition?"}
{"completion": " The Latex Code for equation Equation of Exchangeis <equation>\\\\text{MV} = \\\\text{PQ}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Equation of Exchange?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>S</equation> in Future Value of Ordinary Annuities is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>S</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: Early Exercise getting the stock's dividend payments.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Calls and Puts with Different Strikes is: <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. Here is the brief introduction of Calls and Puts with Different Strikes:\n\n        Latex code for the Calls and Puts with Different Strikes. For European calls and puts, with strike prices K_{1} and K_{2}, where K_{1} < K_{2}, we know the following.\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\n            American options, For three different options with strike prices K1 < K2 < K3:\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand is: Percentage change in quantity demanded.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Monte-Carlo Simulationsis <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Monte-Carlo Simulations?"}
{"completion": " The equation for Tax Multiplier is: <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>. Here is the brief introduction of Tax Multiplier:\n        Latex code for Tax Multiplier.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Tax Multiplier?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TVC}</equation> in Total Costs is: Total Variable Costs (TVC).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{TVC}</equation> in Total Costs?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>AP</equation> in Average Product is: Average Product.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>AP</equation> in Average Product?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>A(T)</equation> in Asian Options is: Arithmetic average of option price at time T.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>A(T)</equation> in Asian Options?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{C}</equation> in Distributive Efficiency Condition is: Product of C.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Gini Coefficientis <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Gini Coefficient?"}
{"completion": " The equation for Elasticity of Supply is: <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>. Here is the brief introduction of Elasticity of Supply:\n        Latex code for Elasticity of Supply. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Elasticity of Supply?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>QI</equation> in Average Product is: Quantity of Input.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>QI</equation> in Average Product?"}
{"completion": " The equation for Compound Interest is: <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. Here is the brief introduction of Compound Interest:\n        Latex code for the Compound Interest. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Maturity Value\n: Principal/Present Value\n: Annual Rate (decimal)\n: Number of Compounding Periods per Year\n: Time (years)\n: Loan/investment is compounded continuously\n\n\nRelated Documents\n\nCompound Interest Calculator\nInvestopedia Compound Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "I am interested in Compound Interest?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>QI</equation> in Average Product is: Quantity of Input.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>QI</equation> in Average Product?"}
{"completion": " The Latex Code for equation Socially Optimal Level of Outputis <equation>\\\\text{MSB} = \\\\text{MSC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Socially Optimal Level of Output?"}
{"completion": " The equation for Profit-Maximizing Output Level is: <equation>MR = MC</equation>. Here is the brief introduction of Profit-Maximizing Output Level:\n        Latex code for Profit-Maximizing Output Level.\n        \n: Marginal Revenue\n: Marginal Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Profit-Maximizing Output Level?"}
{"completion": " The equation for Compound Interest is: <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. Here is the brief introduction of Compound Interest:\n        Latex code for the Compound Interest. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Maturity Value\n: Principal/Present Value\n: Annual Rate (decimal)\n: Number of Compounding Periods per Year\n: Time (years)\n: Loan/investment is compounded continuously\n\n\nRelated Documents\n\nCompound Interest Calculator\nInvestopedia Compound Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you explain Compound Interest?"}
{"completion": " The equation for Effective Rate is: <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. Here is the brief introduction of Effective Rate:\n        Latex code for the Effective Rate. I will briefly introduce the notations in this formulation. \n        \n: Effective Rate\n: Compute the effective rate if your loan/investment is compounded m times per year.\n: Compute the effective rate if your loan/investment is compounded continuously.\n\n\nRelated Documents\n\nInvestopedia Effective Rate\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you give me a brief introduction to Effective Rate?"}
{"completion": " The related materials of Elasticity of Supply is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Elasticity of Supply?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The Latex Code for equation Tax Multiplieris <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Tax Multiplier?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>Q_{i}</equation> in Gini Coefficient is: The ratio of cumulative i-th group's income(increasing order)/total income.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>Q_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Present Value of Ordinary Annuitiesis <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>", "tag": "Economics", "prompt": "What is the latex code of equation Present Value of Ordinary Annuities?"}
{"completion": " The equation for Merchandise Trade Balance is: <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>. Here is the brief introduction of Merchandise Trade Balance:\n        Latex code for Merchandise Trade Balance.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Merchandise Trade Balance?"}
{"completion": " The related materials of Black-Derman-Toy BDT is: 1.A Binomial Interest Rate Model and the Black-Derman-Toy Model:<url>https://web.ma.utexas.edu/users/mcudina/Lecture24_4and5.pdf</url>;2.Black-Derman-Toy Model Developed by Team at Goldman Sachs:<url>https://www.goldmansachs.com/our-firm/history/moments/1986-black-derman-toy-model.html</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Calls and Puts Arbitrageis <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Calls and Puts Arbitrage?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Optimal Combination of Resources Condition is: Price.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Allocative Efficiency Condition is: <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. Here is the brief introduction of Allocative Efficiency Condition:\n        Latex code for the Allocative Efficiency Condition. I will briefly introduce the notations in this formulation.  \n        Allocative efficiency occurs when consumer demand is completely met by supply. In other words, businesses are providing the exact supply that consumers want.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\nAllocative Efficiency: Definition, Example Productive Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Allocative Efficiency Condition?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>AP</equation> in Average Product is: Average Product.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>AP</equation> in Average Product?"}
{"completion": " The equation for Ito Lemma is: <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. Here is the brief introduction of Ito Lemma:\n        Latex code for the Ito Lemma.\n        \n: Diffusion\n: Stochastic differential equation for X(t)\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Ito Lemma?"}
{"completion": " The Latex Code for equation Nominal Interest Rateis <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Nominal Interest Rate?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{PQ}</equation> in Equation of Exchange is: Total spending on goods and services, measured as PY (or nominal GDP).", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>\\text{PQ}</equation> in Equation of Exchange?"}
{"completion": " The Latex Code for equation Put-Call Parityis <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Put-Call Parity?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Variable Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>Q</equation> in Average Variable Cost?"}
{"completion": " The Latex Code for equation Average Total Costis <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Average Total Cost?"}
{"completion": " The equation for Ito Lemma is: <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. Here is the brief introduction of Ito Lemma:\n        Latex code for the Ito Lemma.\n        \n: Diffusion\n: Stochastic differential equation for X(t)\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Ito Lemma?"}
{"completion": " The Latex Code for equation Elasticity of Supplyis <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Elasticity of Supply?"}
{"completion": " The Latex Code for equation Equality of Leakages and Injectionsis <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Equality of Leakages and Injections?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{B}</equation> in Gini Coefficient is: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income)..", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>S_{B}</equation> in Gini Coefficient?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of call option c.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Calls and Puts Arbitrage is: <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. Here is the brief introduction of Calls and Puts Arbitrage:\n\n        Latex code for the Calls and Puts Arbitrage. Three different options have strike prices K1, K2, K3 and K1 < K2 < K3 holds.\n        An important formula for determining arbitrage opportunities comes from the following equations.\n        \n\n: Strike price of option 1\n: Strike price of option 2\n: Strike price of option 3\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Calls and Puts Arbitrage?"}
{"completion": " The equation for Production Efficiency Condition is: <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. Here is the brief introduction of Production Efficiency Condition:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal Product Label\n\n\nRelated Documents\n\nProduction Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Production Efficiency Condition?"}
{"completion": " The Latex Code for equation Forwardsis <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Forwards?"}
{"completion": " The equation for Standard Brownian Motion is: <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. Here is the brief introduction of Standard Brownian Motion:\n        Latex code for the Standard Brownian Motion. I will briefly introduce the notations in this formulation. {Z(t)} has independent increments, and {Z(t)} has stationary increments such that Z (t + s) ? Z (t) follows standard normal distribution\n        \n: Value of Z at time stamp t\n: Stationary increments of Standard Brownian Motion\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Standard Brownian Motion?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>t</equation> in Simple Interest is: Time (years).", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>t</equation> in Simple Interest?"}
{"completion": " The equation for Profit-Maximizing Output Level is: <equation>MR = MC</equation>. Here is the brief introduction of Profit-Maximizing Output Level:\n        Latex code for Profit-Maximizing Output Level.\n        \n: Marginal Revenue\n: Marginal Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Profit-Maximizing Output Level?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Marginal Factor Cost MFCis <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Marginal Factor Cost MFC?"}
{"completion": " The Latex Code for equation Calls and Puts Arbitrageis <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Calls and Puts Arbitrage?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\delta</equation> in Sharpe Ratio is: Compounded Dividend Rate.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\delta</equation> in Sharpe Ratio?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>g_{i}</equation> in Monte-Carlo Simulations is: The i-th simulated payoff.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>g_{i}</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Optimal Consumption Ruleis <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Optimal Consumption Rule?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>n</equation> in Annuities Due is: Total number of times compounded.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>n</equation> in Annuities Due?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>A(T)</equation> in Asian Options is: Arithmetic average of option price at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>A(T)</equation> in Asian Options?"}
{"completion": " The equation for Gross Domestic Product Deflator is: <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Gross Domestic Product Deflator:\n        Latex code for Gross Domestic Product Deflator.\n        \n \n\nRelated Documents\n\nCorporate Finance Institute GDP Formula\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Gross Domestic Product Deflator?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>n</equation> in Annuities Due is: Total number of times compounded.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>n</equation> in Annuities Due?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(0, S)</equation> in Bonds and Interest Rates is: Price of an s-year zero..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P(0, S)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Average Product is: <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. Here is the brief introduction of Average Product:\n        Latex code for the Average Product. I will briefly introduce the notations in this formulation.  \n        \n: Average Product\n: Total Product\n: Quantity of Input\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Average Product?"}
{"completion": " The Latex Code for equation Monte-Carlo Simulationsis <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Monte-Carlo Simulations?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>F_{t,T}(S)</equation> in Forwards is: Forward Contract at strike price S.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>F_{t,T}(S)</equation> in Forwards?"}
{"completion": " The related materials of Real Interest Rate is: 1.Merchandise imports:<url>https://data.worldbank.org/indicator/TM.VAL.MRCH.CD.WT</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Real Interest Rate?"}
{"completion": " The related materials of Gross Domestic Product Deflator is: 1.Corporate Finance Institute GDP Formula:<url>https://corporatefinanceinstitute.com/resources/economics/gdp-formula/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Gross Domestic Product Deflator?"}
{"completion": " The related materials of Calls and Puts with Different Strikes is: 1.Investopedia Put Call Parity:<url>https://www.investopedia.com/terms/p/putcallparity.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Profit-Maximizing Output Levelis <equation>MR = MC</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Profit-Maximizing Output Level?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{A}</equation> in Gini Coefficient is: Area between Line of Perfect Equality and Lorenz Curve..", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>S_{A}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Calls and Puts Arbitrageis <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Calls and Puts Arbitrage?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>t</equation> in Simple Interest is: Time (years).", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>t</equation> in Simple Interest?"}
{"completion": " The equation for Sharpe Ratio is: <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. Here is the brief introduction of Sharpe Ratio:\n        Latex code for Sharpe Ratio.\n        \n: Compounded Dividend Rate\n: Sharpe ratio\n: Sharpe ratio of any asset written on a GBM\n\n\nRelated Documents\n\nSharpe Ratio Formula and Definition With Examples\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Sharpe Ratio?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>ATC</equation> in Average Total Cost is: Average Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>ATC</equation> in Average Total Cost?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MR</equation> in Marginal Revenue?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>Q</equation> in Marginal Cost is: Quantity.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>Q</equation> in Marginal Cost?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>m</equation> in Compound Interest is: Number of Compounding Periods per Year.", "tag": "Economics", "prompt": "What does the symbol mean <equation>m</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Marginal Revenueis <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Marginal Revenue?"}
{"completion": " The Latex Code for equation Profit-Maximizing Output Levelis <equation>MR = MC</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Profit-Maximizing Output Level?"}
{"completion": " The Latex Code for equation Simple Interestis <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>", "tag": "Economics", "prompt": "What is the equation of Simple Interest?"}
{"completion": " The Latex Code for equation Balanced Budget Multiplieris <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Balanced Budget Multiplier?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>i</equation> in Future Value of Ordinary Annuities is: Rate per period.", "tag": "Economics", "prompt": "What is the meaning of <equation>i</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity is: .", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded m times per year..", "tag": "Economics", "prompt": "What is the meaning of <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate?"}
{"completion": " The Latex Code for equation Real GDPis <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Real GDP?"}
{"completion": " The Latex Code for equation Geometric Brownian Motionis <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Geometric Brownian Motion?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e}</equation> in Effective Rate is: Effective Rate.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>r_{e}</equation> in Effective Rate?"}
{"completion": " The Latex Code for equation Sharpe Ratiois <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Sharpe Ratio?"}
{"completion": " The Latex Code for equation Slope of the Total Product Curveis <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Slope of the Total Product Curve?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Compound Interestis <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>", "tag": "Economics", "prompt": "Can you write equation Compound Interest?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>r</equation> in Compound Interest is: Annual Rate (decimal).", "tag": "Economics", "prompt": "Can you explain the symbol <equation>r</equation> in Compound Interest?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates is: Non-continuous annualized rate.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Slope of the Total Product Curve is: <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. Here is the brief introduction of Slope of the Total Product Curve:\n        Latex code for Slope of the Total Product Curve.\n        \n: Change in Total Product\n: Total Product Curve\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Slope of the Total Product Curve?"}
{"completion": " The Latex Code for equation Risk-Neutral Valuation and Power Contractsis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPS</equation> in Autonomous Spending Multiplier is: Marginal Propensity Save.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>MPS</equation> in Autonomous Spending Multiplier?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{1}.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections is: Exports.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>\\text{X}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of call option c.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\mu</equation> in Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Unemployment Rateis <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Unemployment Rate?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>MPL</equation> in Marginal Product of Labor is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MPL</equation> in Marginal Product of Labor?"}
{"completion": " The equation for Average Product is: <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. Here is the brief introduction of Average Product:\n        Latex code for the Average Product. I will briefly introduce the notations in this formulation.  \n        \n: Average Product\n: Total Product\n: Quantity of Input\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Average Product?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P_{1}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Geometric Brownian Motion SDEsis <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. Here is the brief introduction of Stock Prices as Geometric Brownian Motion:\n        Latex code for Stock Prices as Geometric Brownian Motion.\n        \n: Observed stock price S(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Average Variable Cost is: <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Variable Cost:\n        Latex code for the Average Variable Cost. I will briefly introduce the notations in this formulation.  \n        \n: Average Variable Cost\n: Total Variable Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Average Variable Cost?"}
{"completion": " The Latex Code for equation Sharpe Ratiois <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Sharpe Ratio?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Elasticity of Supply is: <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>. Here is the brief introduction of Elasticity of Supply:\n        Latex code for Elasticity of Supply. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Elasticity of Supply?"}
{"completion": " The Latex Code for equation Price Elasticity of Demandis <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Price Elasticity of Demand?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>\\text{I}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Price Elasticity of Demand is: <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. Here is the brief introduction of Price Elasticity of Demand:\n        Latex code for Price Elasticity of Demand. Price Elasticity of Demand= Percentage change in quantity demanded / Percentage change in Price\n        \n: Percentage change in quantity demanded\n: Percentage change in Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Price Elasticity of Demand?"}
{"completion": " The equation for Sharpe Ratio is: <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. Here is the brief introduction of Sharpe Ratio:\n        Latex code for Sharpe Ratio.\n        \n: Compounded Dividend Rate\n: Sharpe ratio\n: Sharpe ratio of any asset written on a GBM\n\n\nRelated Documents\n\nSharpe Ratio Formula and Definition With Examples\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Sharpe Ratio?"}
{"completion": " The Latex Code for equation Average Total Costis <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Average Total Cost?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\mu</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>U</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{B}</equation> in Gini Coefficient is: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income)..", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>S_{B}</equation> in Gini Coefficient?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>Q</equation> in Average Fixed Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>Q</equation> in Average Fixed Cost?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{2}.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor is: Change in Labor(L).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Factor of Production Hiring Ruleis <equation>\\\\text{MRP} = \\\\text{MFC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Factor of Production Hiring Rule?"}
{"completion": " The Latex Code for equation Compound Interestis <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>", "tag": "Economics", "prompt": "What is the latex code of equation Compound Interest?"}
{"completion": " The Latex Code for equation Distributive Efficiency Conditionis <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Distributive Efficiency Condition?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Socially Optimal Level of Output is: <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. Here is the brief introduction of Socially Optimal Level of Output:\n        Latex code for Socially Optimal Level of Output.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Socially Optimal Level of Output?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TFC}</equation> in Total Costs is: Total Fixed Costs (TFC).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{TFC}</equation> in Total Costs?"}
{"completion": " The Latex Code for equation Monte-Carlo Simulationsis <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Monte-Carlo Simulations?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>R</equation> in Annuities Due is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "What does the symbol mean <equation>R</equation> in Annuities Due?"}
{"completion": " The equation for Merchandise Trade Balance is: <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>. Here is the brief introduction of Merchandise Trade Balance:\n        Latex code for Merchandise Trade Balance.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Merchandise Trade Balance?"}
{"completion": " The related materials of Equation of Exchange is: 1.Monetary Policy and the Equation of Exchange:<url>https://open.lib.umn.edu/macroeconomics/chapter/11-3-monetary-policy-and-the-equation-of-exchange/</url>;2.Investopedia: equation of exchange:<url>https://www.investopedia.com/terms/e/equation_of_exchange.asp</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Equation of Exchange?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{P}</equation> in Investment is: Planned investment.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>I_{P}</equation> in Investment?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(0, S)</equation> in Bonds and Interest Rates is: Price of an s-year zero..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P(0, S)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Annuities Due is: <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. Here is the brief introduction of Annuities Due:\n        Latex code for the Future Value of Annuities Due. I will briefly introduce the notations in this formulation. \n        The payment/deposit is at the BEGINNING of the period\n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Please give me detailed tutorial of Annuities Due?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The related materials of Marginal Revenue Product is: 1.The Demand for Labor:<url>https://open.lib.umn.edu/principleseconomics/chapter/12-1-the-demand-for-labor/</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Marginal Revenue Product?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Slope of the Total Product Curve is: <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. Here is the brief introduction of Slope of the Total Product Curve:\n        Latex code for Slope of the Total Product Curve.\n        \n: Change in Total Product\n: Total Product Curve\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Slope of the Total Product Curve?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Put Option Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Equation of Exchangeis <equation>\\\\text{MV} = \\\\text{PQ}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Equation of Exchange?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC is: Change in the quantity of the factor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Price Elasticity of Demand is: <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. Here is the brief introduction of Price Elasticity of Demand:\n        Latex code for Price Elasticity of Demand. Price Elasticity of Demand= Percentage change in quantity demanded / Percentage change in Price\n        \n: Percentage change in quantity demanded\n: Percentage change in Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Geometric Brownian Motion SDEsis <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Geometric Brownian Motion SDEs?"}
{"completion": " The related materials of Marginal Cost is: 1.Investopedia Marginal Cost:<url>https://www.investopedia.com/terms/m/marginalcostofproduction.asp</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Marginal Cost?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations is: The variance of stock price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>r</equation> in Forwards is: Interest Rate.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>r</equation> in Forwards?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity is: .", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity?"}
{"completion": " The Latex Code for equation Calls and Puts with Different Strikesis <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Calls and Puts with Different Strikes?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage is: Strike price of option 3.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The related materials of Ito Lemma is: 1.Geometric Brownian Motion:<url>https://www.quantstart.com/articles/Geometric-Brownian-Motion/</url>;2.Geometric Brownian motion:<url>http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GBM.pdf</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Ito Lemma?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio is: Sharpe ratio.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage is: Strike price of option 1.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Simple Interestis <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>", "tag": "Economics", "prompt": "How to write equation Simple Interest?"}
{"completion": " The Latex Code for equation Marginal Revenue Productis <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Marginal Revenue Product?"}
{"completion": " The related materials of Average Revenue is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Average Revenue?"}
{"completion": " The Latex Code for equation Socially Optimal Level of Outputis <equation>\\\\text{MSB} = \\\\text{MSC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Socially Optimal Level of Output?"}
{"completion": " The Latex Code for equation Real GDPis <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Real GDP?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MSC}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Marginal Revenue Product of Labor MRPL:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Equality of Leakages and Injectionsis <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Equality of Leakages and Injections?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{1}.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Production Efficiency Condition is <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. The meaning of symbol <equation>MP_{L}</equation> in Production Efficiency Condition is: Marginal Product Label.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MP_{L}</equation> in Production Efficiency Condition?"}
{"completion": " The Latex Code for equation Varying Times to Expirationis <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Varying Times to Expiration?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>i</equation> in Present Value of Ordinary Annuities is: Rate per period, usually i=r/m.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>i</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor is: Change in Total Product(TP).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Allocative Efficiency Conditionis <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Allocative Efficiency Condition?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Average Fixed Costis <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Average Fixed Cost?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>I</equation> in Simple Interest is: Interest Earned.", "tag": "Economics", "prompt": "What does the symbol mean <equation>I</equation> in Simple Interest?"}
{"completion": " The equation for Real Interest Rate is: <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Real Interest Rate:\n        Latex code for Real Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Real Interest Rate?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Optimal Combination of Resources Conditionis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Optimal Combination of Resources Condition?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>t</equation> in Compound Interest is: Time (years).", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>t</equation> in Compound Interest?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>G(T)</equation> in Asian Options is: Geometric average of option price at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>G(T)</equation> in Asian Options?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(T)</equation> in Monte-Carlo Simulations is: The stock price at time T.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>S(T)</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor is: Change in Total Product(TP).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>P</equation> in Optimal Consumption Rule is: Price.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MR</equation> in Marginal Revenue?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor is: Change in Labor(L).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor?"}
{"completion": " The related materials of Marginal Revenue is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Marginal Revenue?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: Early Exercise getting the stock's dividend payments.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Monte-Carlo Simulations is: <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. Here is the brief introduction of Monte-Carlo Simulations:\n        Latex code for the Monte-Carlo Simulations of stock prices. I will briefly introduce the notations in this formulation. Monte-Carlo simulation simulates stock prices, calculate the payoff the option for each of those simulated prices, find the average payoff, and then discount the average payoff. Firstly, we start with iid uniform numbers u_{1} to u_{n}, calculate standard normal variable z_{i} as , convert to normal variable .  The variance of the Monte-Carlo estimate is calculated as . \n        \n: The stock price at time T\n: The stock price at time t, which is nearer to final stage stock price S(T)\n: The i-th simulated payoff\n: The variance of stock price\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Average Revenueis <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Average Revenue?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\delta</equation> in Sharpe Ratio is: Compounded Dividend Rate.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\delta</equation> in Sharpe Ratio?"}
{"completion": " The equation for Merchandise Trade Balance is: <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>. Here is the brief introduction of Merchandise Trade Balance:\n        Latex code for Merchandise Trade Balance.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Merchandise Trade Balance?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>Y(t)</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Marginal Revenue Product is: <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. Here is the brief introduction of Marginal Revenue Product:\n        Latex code for Marginal Revenue Product. The amount that an additional unit of a factor adds to a firm's total revenue during a period is called the marginal revenue product (MRP) of the factor. An additional unit of a factor of production adds to a firm\u2019s revenue in a two-step process: first, it increases the firm's output. Second, the increased output increases the firm\u2019s total revenue. We find marginal revenue product by multiplying the marginal product (MP) of the factor by the marginal revenue (MR). I will briefly introduce the notations in this formulation.  \n        \n: Marginal Product(MP)\n: Marginal Revenue(MR)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Marginal Revenue Product?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>n</equation> in Annuities Due is: Total number of times compounded.", "tag": "Economics", "prompt": "What does the symbol mean <equation>n</equation> in Annuities Due?"}
{"completion": " The equation for Forwards is: <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. Here is the brief introduction of Forwards:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. A forward contract is an agreement in which the buyer agrees at time t to pay the seller at time T and receive the asset at time T.\n        \n: Forward Contract at strike price S\n: Interest Rate\n: Future Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Forwards?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>S</equation> in Future Value of Ordinary Annuities is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "What does the symbol mean <equation>S</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage is: Strike price of option 2.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Calls and Puts Arbitrage is: <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. Here is the brief introduction of Calls and Puts Arbitrage:\n\n        Latex code for the Calls and Puts Arbitrage. Three different options have strike prices K1, K2, K3 and K1 < K2 < K3 holds.\n        An important formula for determining arbitrage opportunities comes from the following equations.\n        \n\n: Strike price of option 1\n: Strike price of option 2\n: Strike price of option 3\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Calls and Puts Arbitrage?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Marginal Revenue Product of Labor MRPL:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Real GDPis <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Real GDP?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Total Cost is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>TC</equation> in Average Total Cost?"}
{"completion": " The related materials of Average Variable Cost is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Average Variable Cost?"}
{"completion": " The equation for Average Fixed Cost is: <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. Here is the brief introduction of Average Fixed Cost:\n        Latex code for the Allocative Average Fixed Cost. I will briefly introduce the notations in this formulation.  \n        \n: Total Fixed Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Average Fixed Cost?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{B}</equation> in Gini Coefficient is: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income)..", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>S_{B}</equation> in Gini Coefficient?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The related materials of Asian Options is: 1.What Is an Asian Option? How They Work Vs. Standard Options:<url>https://www.investopedia.com/terms/a/asianoption.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Asian Options?"}
{"completion": " The Latex Code for equation Sharpe Ratiois <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Sharpe Ratio?"}
{"completion": " The Latex Code for equation Average Variable Costis <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Average Variable Cost?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>R</equation> in Future Value of Ordinary Annuities is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>R</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Annuities Dueis <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>", "tag": "Economics", "prompt": "How to write equation Annuities Due?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{PQ}</equation> in Equation of Exchange is: Total spending on goods and services, measured as PY (or nominal GDP).", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>\\text{PQ}</equation> in Equation of Exchange?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\delta</equation> in Sharpe Ratio is: Compounded Dividend Rate.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\delta</equation> in Sharpe Ratio?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity is: the present value of the strike price (x),.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity?"}
{"completion": " The Latex Code for equation Real GDPis <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Real GDP?"}
{"completion": " The related materials of Tax Multiplier is: 1.Merchandise imports:<url>https://data.worldbank.org/indicator/TM.VAL.MRCH.CD.WT</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Tax Multiplier?"}
{"completion": " The Latex Code for equation Marginal Factor Cost MFCis <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Marginal Factor Cost MFC?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Asian Options is: <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. Here is the brief introduction of Asian Options:\n        Latex code for the Asian options are options. Asian options are options that are based on averages in place of either the price or the strike. The average can be either an arithmetic average or a geometric average. Then to price the option replace either the strike or the price with the appropriate path-dependent average, calculate the payoffs, and then discount them.\n        \n: Arithmetic average of option price at time T\n: Geometric average of option price at time T\n\n\nRelated Documents\n\nWhat Is an Asian Option? How They Work Vs. Standard Options\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Asian Options?"}
{"completion": " The Latex Code for equation Average Total Costis <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Average Total Cost?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MP</equation> in Marginal Revenue Product is: Marginal Product(MP).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MP</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts is: Price of the power contract.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded m times per year..", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of put option p.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The Latex Code for equation Investmentis <equation>I=I_{P}+I_{U}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Investment?"}
{"completion": " The equation for Compound Interest is: <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. Here is the brief introduction of Compound Interest:\n        Latex code for the Compound Interest. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Maturity Value\n: Principal/Present Value\n: Annual Rate (decimal)\n: Number of Compounding Periods per Year\n: Time (years)\n: Loan/investment is compounded continuously\n\n\nRelated Documents\n\nCompound Interest Calculator\nInvestopedia Compound Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you give me a brief introduction to Compound Interest?"}
{"completion": " The equation for Slope of the Total Product Curve is: <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. Here is the brief introduction of Slope of the Total Product Curve:\n        Latex code for Slope of the Total Product Curve.\n        \n: Change in Total Product\n: Total Product Curve\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Slope of the Total Product Curve?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts is: Payoff a power contract at time T.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The related materials of Optimal Consumption Rule is: 1.How Is the Marginal Product of Labor Determined:<url>https://economics.stackexchange.com/questions/14639/determining-optimal-consumption-bundle</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Optimal Consumption Rule?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>i</equation> in Annuities Due is: Rate per period.", "tag": "Economics", "prompt": "What is the meaning of <equation>i</equation> in Annuities Due?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>MPL</equation> in Marginal Product of Labor is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MPL</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Nominal Interest Rateis <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Nominal Interest Rate?"}
{"completion": " The equation for Future Value of Ordinary Annuities is: <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. Here is the brief introduction of Future Value of Ordinary Annuities:\n        Latex code for the Future Value of Ordinary Annuities. The payment/deposit is at the END of the period. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you give me a brief introduction to Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Slope of the Total Product Curveis <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Slope of the Total Product Curve?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The related materials of Price Elasticity of Demand is: 1.Investopedia Price Elasticity of Demand:<url>https://www.investopedia.com/terms/p/priceelasticity.asp</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Price Elasticity of Demand?"}
{"completion": " The equation for Balanced Budget Multiplier is: <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. Here is the brief introduction of Balanced Budget Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Balanced Budget Multiplier?"}
{"completion": " The equation for Slope of the Total Product Curve is: <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. Here is the brief introduction of Slope of the Total Product Curve:\n        Latex code for Slope of the Total Product Curve.\n        \n: Change in Total Product\n: Total Product Curve\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Slope of the Total Product Curve?"}
{"completion": " The related materials of Marginal Revenue Product of Labor MRPL is: 1.How Is the Marginal Product of Labor Determined:<url>https://www.masterclass.com/articles/learn-about-marginal-product-of-labor-in-economics</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Geometric Brownian Motionis <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Geometric Brownian Motion?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(0, S)</equation> in Bonds and Interest Rates is: Price of an s-year zero..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P(0, S)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Asian Options is: <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. Here is the brief introduction of Asian Options:\n        Latex code for the Asian options are options. Asian options are options that are based on averages in place of either the price or the strike. The average can be either an arithmetic average or a geometric average. Then to price the option replace either the strike or the price with the appropriate path-dependent average, calculate the payoffs, and then discount them.\n        \n: Arithmetic average of option price at time T\n: Geometric average of option price at time T\n\n\nRelated Documents\n\nWhat Is an Asian Option? How They Work Vs. Standard Options\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Asian Options?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TR}</equation> in Profit is: Total Revenue.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{TR}</equation> in Profit?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>P</equation> in Price for a Competitive Firm is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Price for a Competitive Firm?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>Q</equation> in Marginal Cost is: Quantity.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>Q</equation> in Marginal Cost?"}
{"completion": " The related materials of Sharpe Ratio is: 1.Sharpe Ratio Formula and Definition With Examples:<url>https://www.investopedia.com/terms/s/sharperatio.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Sharpe Ratio?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e}</equation> in Effective Rate is: Effective Rate.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>r_{e}</equation> in Effective Rate?"}
{"completion": " The equation for Merchandise Trade Balance is: <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>. Here is the brief introduction of Merchandise Trade Balance:\n        Latex code for Merchandise Trade Balance.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Merchandise Trade Balance?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>R</equation> in Annuities Due is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>R</equation> in Annuities Due?"}
{"completion": " The Latex Code for equation Marginal Costis <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Marginal Cost?"}
{"completion": " The equation for Bonds and Interest Rates is: <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. Here is the brief introduction of Bonds and Interest Rates:\n        Latex code for the Bonds and Interest Rates. The price of an s-year zero is P(0, S). The forward bond price formula  is calculated as . And the \n        non-continuous annualized rate is .\n        \n: Price of an s-year zero.\n: Forward Bond Price\n: Non-continuous annualized rate\n\n\nRelated Documents\n\nBond and Interest Rate\nUnderstanding Interest Rates, Inflation, and Bonds\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Bonds and Interest Rates?"}
{"completion": " The related materials of Calls and Puts Arbitrage is: 1.Investopedia Put Call Parity:<url>https://www.investopedia.com/terms/p/putcallparity.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Black-Derman-Toy BDTis <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Black-Derman-Toy BDT?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve is: Change in Total Product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve?"}
{"completion": " The Latex Code for equation Annuities Dueis <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>", "tag": "Economics", "prompt": "Show me the latex code of equation Annuities Due?"}
{"completion": " The Latex Code for equation Stock Prices as Geometric Brownian Motionis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>P_{i}</equation> in Gini Coefficient is: The ratio of i-th group's population(P)/total population(P).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Gross Domestic Product Deflator is: <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Gross Domestic Product Deflator:\n        Latex code for Gross Domestic Product Deflator.\n        \n \n\nRelated Documents\n\nCorporate Finance Institute GDP Formula\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Gross Domestic Product Deflator?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve is: Total Product Curve.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{TPC}</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>U</equation> in Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Unemployment Rateis <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Unemployment Rate?"}
{"completion": " The equation for Average Total Cost is: <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Total Cost:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n: Average Total Cost\n: Total Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Average Total Cost?"}
{"completion": " The equation for Present Value of Ordinary Annuities is: <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. Here is the brief introduction of Present Value of Ordinary Annuities:\n        Latex code for the Present Value of Ordinary Annuities. I will briefly introduce the notations in this formulation.  \n        The payment is made at the END of the period. \n        \n: Present Value\n: Payment made in each period\n: Rate per period, usually i=r/m\n: Total number of times compounded, n=mt\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Please give me detailed tutorial of Present Value of Ordinary Annuities?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPS</equation> in Autonomous Spending Multiplier is: Marginal Propensity Save.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>MPS</equation> in Autonomous Spending Multiplier?"}
{"completion": " The Latex Code for equation Price Elasticity of Demandis <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Price Elasticity of Demand?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TR}</equation> in Profit is: Total Revenue.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{TR}</equation> in Profit?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{A}</equation> in Gini Coefficient is: Area between Line of Perfect Equality and Lorenz Curve..", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>S_{A}</equation> in Gini Coefficient?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I</equation> in Investment is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>I</equation> in Investment?"}
{"completion": " The equation for Nominal Interest Rate is: <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Nominal Interest Rate:\n        Latex code for Nominal Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Nominal Interest Rate?"}
{"completion": " The Latex Code for equation Standard Brownian Motionis <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Standard Brownian Motion?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Early Exercise for American Options is: <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. Here is the brief introduction of Early Exercise for American Options:\n\n            So we exercise the call option if the pros are greater than the cons, specifically, we exercise if:\n        \n\n: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons. \n: Early Exercise getting the stock's dividend payments\n: Pay the strike earlier and therefore miss the interest on that money\n: put protection if the stock price should fall.\n: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise. \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Early Exercise for American Options?"}
{"completion": " The equation for Early Exercise for American Options is: <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. Here is the brief introduction of Early Exercise for American Options:\n\n            So we exercise the call option if the pros are greater than the cons, specifically, we exercise if:\n        \n\n: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons. \n: Early Exercise getting the stock's dividend payments\n: Pay the strike earlier and therefore miss the interest on that money\n: put protection if the stock price should fall.\n: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise. \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Gini Coefficientis <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Gini Coefficient?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{MV}</equation> in Equation of Exchange is: Total spending on goods and services, measured as Monetary Value.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MV}</equation> in Equation of Exchange?"}
{"completion": " The Latex Code for equation Forwardsis <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Forwards?"}
{"completion": " The equation for Balanced Budget Multiplier is: <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. Here is the brief introduction of Balanced Budget Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Balanced Budget Multiplier?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Call and Put Price Boundsis <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Call and Put Price Bounds?"}
{"completion": " The equation for Average Revenue is: <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>. Here is the brief introduction of Average Revenue:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Average Revenue?"}
{"completion": " The equation for Gross Domestic Product Deflator is: <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Gross Domestic Product Deflator:\n        Latex code for Gross Domestic Product Deflator.\n        \n \n\nRelated Documents\n\nCorporate Finance Institute GDP Formula\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Gross Domestic Product Deflator?"}
{"completion": " The equation for Consumption Function is: <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>. Here is the brief introduction of Consumption Function:\n        Latex code for Consumption Function.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Consumption Function?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage is: Strike price of option 1.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Production Efficiency Conditionis <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Production Efficiency Condition?"}
{"completion": " The equation for Unemployment Rate is: <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>. Here is the brief introduction of Unemployment Rate:\n        Latex code for Unemployment Rate.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Unemployment Rate?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I</equation> in Investment is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>I</equation> in Investment?"}
{"completion": " The related materials of Marginal Factor Cost MFC is: 1.How Is the Marginal Product of Labor Determined:<url>https://www.masterclass.com/articles/learn-about-marginal-product-of-labor-in-economics</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Marginal Factor Cost MFC?"}
{"completion": " The Latex Code for equation Elasticity of Supplyis <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Elasticity of Supply?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>P</equation> in Simple Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "What does the symbol mean <equation>P</equation> in Simple Interest?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TFC}</equation> in Total Costs is: Total Fixed Costs (TFC).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{TFC}</equation> in Total Costs?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost is: Change in Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{TC}</equation> in Marginal Cost?"}
{"completion": " The equation for Effective Rate is: <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. Here is the brief introduction of Effective Rate:\n        Latex code for the Effective Rate. I will briefly introduce the notations in this formulation. \n        \n: Effective Rate\n: Compute the effective rate if your loan/investment is compounded m times per year.\n: Compute the effective rate if your loan/investment is compounded continuously.\n\n\nRelated Documents\n\nInvestopedia Effective Rate\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you explain Effective Rate?"}
{"completion": " The Latex Code for equation Allocative Efficiency Conditionis <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Allocative Efficiency Condition?"}
{"completion": " The Latex Code for equation Profit-Maximizing Output Levelis <equation>MR = MC</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Profit-Maximizing Output Level?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>Y(t)</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{PQ}</equation> in Equation of Exchange is: Total spending on goods and services, measured as PY (or nominal GDP).", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{PQ}</equation> in Equation of Exchange?"}
{"completion": " The related materials of Average Fixed Cost is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Average Fixed Cost?"}
{"completion": " The Latex Code for equation Bonds and Interest Ratesis <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Bonds and Interest Rates?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>i</equation> in Future Value of Ordinary Annuities is: Rate per period.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>i</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The Latex Code for equation Asian Optionsis <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Asian Options?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Autonomous Spending Multiplieris <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Autonomous Spending Multiplier?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC is: Change in the quantity of the factor.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The Latex Code for equation Factor of Production Hiring Ruleis <equation>\\\\text{MRP} = \\\\text{MFC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Factor of Production Hiring Rule?"}
{"completion": " The related materials of Equality of Leakages and Injections is: 1.Why are leakages equal to injections?:<url>https://wise-answer.com/why-are-leakages-equal-to-injections</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Equality of Leakages and Injections?"}
{"completion": " The equation for Production Efficiency Condition is <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. The meaning of symbol <equation>MP_{L}</equation> in Production Efficiency Condition is: Marginal Product Label.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MP_{L}</equation> in Production Efficiency Condition?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>A</equation> in Simple Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Simple Interest?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>g_{i}</equation> in Monte-Carlo Simulations is: The i-th simulated payoff.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>g_{i}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of call option c.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The Latex Code for equation Marginal Product of Laboris <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Marginal Product of Labor?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion is: Stationary increments of Standard Brownian Motion.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The Latex Code for equation Forwardsis <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Forwards?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>\\text{I}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>I</equation> in Simple Interest is: Interest Earned.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>I</equation> in Simple Interest?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Variable Cost is: Total Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>TC</equation> in Average Variable Cost?"}
{"completion": " The Latex Code for equation Marginal Factor Cost MFCis <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Marginal Factor Cost MFC?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve is: Change in Total Product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta Q</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Profit is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{TC}</equation> in Profit?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>m</equation> in Compound Interest is: Number of Compounding Periods per Year.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>m</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Real Interest Rateis <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Real Interest Rate?"}
{"completion": " The Latex Code for equation Gross Domestic Product Deflatoris <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Gross Domestic Product Deflator?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Stock Prices as Geometric Brownian Motionis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>ATC</equation> in Average Total Cost is: Average Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>ATC</equation> in Average Total Cost?"}
{"completion": " The Latex Code for equation Banks Reserve Ratiois <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Profitis <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Profit?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio is: Sharpe ratio.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio?"}
{"completion": " The Latex Code for equation Consumption Functionis <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Consumption Function?"}
{"completion": " The Latex Code for equation Optimal Consumption Ruleis <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Optimal Consumption Rule?"}
{"completion": " The equation for Gini Coefficient is: <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. Here is the brief introduction of Gini Coefficient:\n        Latex code for Gini Coefficient.  The Gini coefficient (Gini index or Gini ratio) is a statistical measure of economic inequality in a population. The coefficient measures the dispersion of income or distribution of wealth among the members of a population.\n        \n: Area between Line of Perfect Equality and Lorenz Curve.\n: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income).\n: The ratio of i-th group's income/total income\n: The ratio of cumulative i-th group's income(increasing order)/total income\n: The ratio of i-th group's population(P)/total population(P)\n\n\nRelated Documents\n\nCorporate Finance Institute Gini-coefficient\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Gini Coefficient?"}
{"completion": " The Latex Code for equation Geometric Brownian Motionis <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Monte-Carlo Simulationsis <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Monte-Carlo Simulations?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TVC}</equation> in Total Costs is: Total Variable Costs (TVC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{TVC}</equation> in Total Costs?"}
{"completion": " The equation for Monte-Carlo Simulations is: <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. Here is the brief introduction of Monte-Carlo Simulations:\n        Latex code for the Monte-Carlo Simulations of stock prices. I will briefly introduce the notations in this formulation. Monte-Carlo simulation simulates stock prices, calculate the payoff the option for each of those simulated prices, find the average payoff, and then discount the average payoff. Firstly, we start with iid uniform numbers u_{1} to u_{n}, calculate standard normal variable z_{i} as , convert to normal variable .  The variance of the Monte-Carlo estimate is calculated as . \n        \n: The stock price at time T\n: The stock price at time t, which is nearer to final stage stock price S(T)\n: The i-th simulated payoff\n: The variance of stock price\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Monte-Carlo Simulations?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: Early Exercise getting the stock's dividend payments.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Equation of Exchange is: <equation>\\\\text{MV} = \\\\text{PQ}</equation>. Here is the brief introduction of Equation of Exchange:\n        Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.\n        \n: Total spending on goods and services, measured as Monetary Value\n: Total spending on goods and services, measured as PY (or nominal GDP)\n\n\nRelated Documents\n\nInvestopedia: equation of exchange\nMonetary Policy and the Equation of Exchange\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Equation of Exchange?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Profit is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{TC}</equation> in Profit?"}
{"completion": " The equation for Average Total Cost is: <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Total Cost:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n: Average Total Cost\n: Total Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Average Total Cost?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost is: Change in Quantity.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{Q}</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Marginal Revenue Product of Labor MRPLis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MRP</equation> in Factor of Production Hiring Rule is: Marginal revenue product.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MRP</equation> in Factor of Production Hiring Rule?"}
{"completion": " The related materials of Risk-Neutral Valuation and Power Contracts is: 1.Geometric Brownian Motion:<url>https://www.quantstart.com/articles/Geometric-Brownian-Motion/</url>;2.Geometric Brownian motion:<url>http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GBM.pdf</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>TFC</equation> in Average Fixed Cost is: Total Fixed Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>TFC</equation> in Average Fixed Cost?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC is: Change in the quantity of the factor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>P</equation> in Optimal Consumption Rule is: Price.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Slope of the Total Product Curve is: <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. Here is the brief introduction of Slope of the Total Product Curve:\n        Latex code for Slope of the Total Product Curve.\n        \n: Change in Total Product\n: Total Product Curve\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Slope of the Total Product Curve?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity is: .", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity?"}
{"completion": " The Latex Code for equation Unemployment Rateis <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Unemployment Rate?"}
{"completion": " The Latex Code for equation Simple Interestis <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>", "tag": "Economics", "prompt": "Show me the latex code of equation Simple Interest?"}
{"completion": " The equation for Equation of Exchange is: <equation>\\\\text{MV} = \\\\text{PQ}</equation>. Here is the brief introduction of Equation of Exchange:\n        Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.\n        \n: Total spending on goods and services, measured as Monetary Value\n: Total spending on goods and services, measured as PY (or nominal GDP)\n\n\nRelated Documents\n\nInvestopedia: equation of exchange\nMonetary Policy and the Equation of Exchange\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Equation of Exchange?"}
{"completion": " The Latex Code for equation Factor of Production Hiring Ruleis <equation>\\\\text{MRP} = \\\\text{MFC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Factor of Production Hiring Rule?"}
{"completion": " The related materials of Monte-Carlo Simulations is: 1.Investopedia Simple Interest:<url>https://www.investopedia.com/terms/s/simple_interest.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Monte-Carlo Simulations?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion is: Observed stock price S(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Unemployment Rateis <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Unemployment Rate?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>r</equation> in Compound Interest is: Annual Rate (decimal).", "tag": "Economics", "prompt": "What does the symbol mean <equation>r</equation> in Compound Interest?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>i</equation> in Annuities Due is: Rate per period.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>i</equation> in Annuities Due?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>i</equation> in Annuities Due is: Rate per period.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>i</equation> in Annuities Due?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>P_{i}</equation> in Gini Coefficient is: The ratio of i-th group's population(P)/total population(P).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Standard Brownian Motionis <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Standard Brownian Motion?"}
{"completion": " The equation for Equation of Exchange is: <equation>\\\\text{MV} = \\\\text{PQ}</equation>. Here is the brief introduction of Equation of Exchange:\n        Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.\n        \n: Total spending on goods and services, measured as Monetary Value\n: Total spending on goods and services, measured as PY (or nominal GDP)\n\n\nRelated Documents\n\nInvestopedia: equation of exchange\nMonetary Policy and the Equation of Exchange\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Equation of Exchange?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TVC}</equation> in Total Costs is: Total Variable Costs (TVC).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{TVC}</equation> in Total Costs?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MFC</equation> in Factor of Production Hiring Rule is: Marginal factor cost (MFC).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MFC</equation> in Factor of Production Hiring Rule?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. Here is the brief introduction of Stock Prices as Geometric Brownian Motion:\n        Latex code for Stock Prices as Geometric Brownian Motion.\n        \n: Observed stock price S(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Investmentis <equation>I=I_{P}+I_{U}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Investment?"}
{"completion": " The Latex Code for equation Black-Derman-Toy BDTis <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Effective Rateis <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>", "tag": "Economics", "prompt": "What is the latex code of equation Effective Rate?"}
{"completion": " The equation for Optimal Combination of Resources Condition is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Optimal Combination of Resources Condition:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Optimal Combination of Resources Condition?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>TC</equation> in Marginal Cost is: Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>TC</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Nominal Interest Rateis <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Nominal Interest Rate?"}
{"completion": " The equation for Marginal Product of Labor is: <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. Here is the brief introduction of Marginal Product of Labor:\n        Latex code for Marginal Product of Labor. \n        \n: Marginal Product of Labor\n: Change in Total Product(TP)\n: Change in Labor(L)\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Marginal Product of Labor?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>MR</equation> in Price for a Competitive Firm is: Marginal revenue (MR).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MR</equation> in Price for a Competitive Firm?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Asian Optionsis <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Asian Options?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>A</equation> in Simple Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>A</equation> in Simple Interest?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>S</equation> in Future Value of Ordinary Annuities is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>S</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Factor of Production Hiring Rule is: <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. Here is the brief introduction of Factor of Production Hiring Rule:\n        Latex code for Factor of Production Hiring Rule. I will briefly introduce the notations in this formulation.  \n        \n: Marginal revenue product\n: Marginal factor cost (MFC)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Factor of Production Hiring Rule?"}
{"completion": " The equation for Marginal Revenue is: <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Revenue:\n        Latex code for Marginal Revenue. \n        \n: Marginal Revenue\n: Change in Total Revenue(TR)\n: Change in Quantity(Q)\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Marginal Revenue?"}
{"completion": " The Latex Code for equation Distributive Efficiency Conditionis <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Distributive Efficiency Condition?"}
{"completion": " The equation for Nominal Interest Rate is: <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Nominal Interest Rate:\n        Latex code for Nominal Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Nominal Interest Rate?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPS</equation> in Autonomous Spending Multiplier is: Marginal Propensity Save.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>MPS</equation> in Autonomous Spending Multiplier?"}
{"completion": " The equation for Price Elasticity of Demand is: <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. Here is the brief introduction of Price Elasticity of Demand:\n        Latex code for Price Elasticity of Demand. Price Elasticity of Demand= Percentage change in quantity demanded / Percentage change in Price\n        \n: Percentage change in quantity demanded\n: Percentage change in Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Price Elasticity of Demand?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor is: Change in Total Product(TP).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Forwardsis <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Forwards?"}
{"completion": " The Latex Code for equation Marginal Costis <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Marginal Cost?"}
{"completion": " The Latex Code for equation Balanced Budget Multiplieris <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Balanced Budget Multiplier?"}
{"completion": " The Latex Code for equation Present Value of Ordinary Annuitiesis <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>", "tag": "Economics", "prompt": "Can you write equation Present Value of Ordinary Annuities?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Price Elasticity of Demand is: <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. Here is the brief introduction of Price Elasticity of Demand:\n        Latex code for Price Elasticity of Demand. Price Elasticity of Demand= Percentage change in quantity demanded / Percentage change in Price\n        \n: Percentage change in quantity demanded\n: Percentage change in Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Slope of the Total Product Curveis <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Slope of the Total Product Curve?"}
{"completion": " The Latex Code for equation Real Interest Rateis <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Real Interest Rate?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>X</equation> in Ito Lemma is: Diffusion.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>X</equation> in Ito Lemma?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity is: .", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts is: Payoff a power contract at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>TC</equation> in Marginal Cost is: Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>TC</equation> in Marginal Cost?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: Early Exercise getting the stock's dividend payments.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Compound Interestis <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>", "tag": "Economics", "prompt": "Show me the latex code of equation Compound Interest?"}
{"completion": " The equation for Average Variable Cost is: <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Variable Cost:\n        Latex code for the Average Variable Cost. I will briefly introduce the notations in this formulation.  \n        \n: Average Variable Cost\n: Total Variable Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Average Variable Cost?"}
{"completion": " The equation for Price for a Competitive Firm is: <equation>P = MR</equation>. Here is the brief introduction of Price for a Competitive Firm:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal revenue (MR)\n: Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Price for a Competitive Firm?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>F_{t,T}(S)</equation> in Forwards is: Forward Contract at strike price S.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>F_{t,T}(S)</equation> in Forwards?"}
{"completion": " The equation for Asian Options is: <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. Here is the brief introduction of Asian Options:\n        Latex code for the Asian options are options. Asian options are options that are based on averages in place of either the price or the strike. The average can be either an arithmetic average or a geometric average. Then to price the option replace either the strike or the price with the appropriate path-dependent average, calculate the payoffs, and then discount them.\n        \n: Arithmetic average of option price at time T\n: Geometric average of option price at time T\n\n\nRelated Documents\n\nWhat Is an Asian Option? How They Work Vs. Standard Options\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Asian Options?"}
{"completion": " The Latex Code for equation Varying Times to Expirationis <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Varying Times to Expiration?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. Here is the brief introduction of Risk-Neutral Valuation and Power Contracts:\n        Latex code for Risk-Neutral Valuation and Power Contracts.\n        \n: Payoff a power contract at time T\n: Price of the power contract\n: Risk-neutral equations\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts is: Payoff a power contract at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio is: Sharpe ratio of any asset written on a GBM.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of call option c.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded m times per year..", "tag": "Economics", "prompt": "Can you explain the symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>FV</equation> in Forwards is: Future Value.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>FV</equation> in Forwards?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>FV</equation> in Forwards is: Future Value.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>FV</equation> in Forwards?"}
{"completion": " The equation for Equality of Leakages and Injections is: <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. Here is the brief introduction of Equality of Leakages and Injections:\n        Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy \u00e2\u20ac\u201c that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.\n        \n: Investment\n: Government Spending\n: Exports\n\n\nRelated Documents\n\nWhy are leakages equal to injections?\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Equality of Leakages and Injections?"}
{"completion": " The equation for Real GDP is: <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>. Here is the brief introduction of Real GDP:\n        Latex code for Real GDP.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Real GDP?"}
{"completion": " The Latex Code for equation Balanced Budget Multiplieris <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Balanced Budget Multiplier?"}
{"completion": " The equation for Ito Lemma is: <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. Here is the brief introduction of Ito Lemma:\n        Latex code for the Ito Lemma.\n        \n: Diffusion\n: Stochastic differential equation for X(t)\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Ito Lemma?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts is: Risk-neutral equations.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Equation of Exchange is: <equation>\\\\text{MV} = \\\\text{PQ}</equation>. Here is the brief introduction of Equation of Exchange:\n        Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.\n        \n: Total spending on goods and services, measured as Monetary Value\n: Total spending on goods and services, measured as PY (or nominal GDP)\n\n\nRelated Documents\n\nInvestopedia: equation of exchange\nMonetary Policy and the Equation of Exchange\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Equation of Exchange?"}
{"completion": " The Latex Code for equation Autonomous Spending Multiplieris <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Autonomous Spending Multiplier?"}
{"completion": " The related materials of Banks Reserve Ratio is: 1.Principles Economics:<url>https://open.lib.umn.edu/principleseconomics/chapter/28-2-the-aggregate-expenditures-model/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Banks Reserve Ratio?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSB</equation> in Allocative Efficiency Condition is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MSB</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>P</equation> in Present Value of Ordinary Annuities is: Present Value.", "tag": "Economics", "prompt": "What is the meaning of <equation>P</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion is: Observed stock price S(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Gini Coefficient is: <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. Here is the brief introduction of Gini Coefficient:\n        Latex code for Gini Coefficient.  The Gini coefficient (Gini index or Gini ratio) is a statistical measure of economic inequality in a population. The coefficient measures the dispersion of income or distribution of wealth among the members of a population.\n        \n: Area between Line of Perfect Equality and Lorenz Curve.\n: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income).\n: The ratio of i-th group's income/total income\n: The ratio of cumulative i-th group's income(increasing order)/total income\n: The ratio of i-th group's population(P)/total population(P)\n\n\nRelated Documents\n\nCorporate Finance Institute Gini-coefficient\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Gini Coefficient?"}
{"completion": " The Latex Code for equation Optimal Consumption Ruleis <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Optimal Consumption Rule?"}
{"completion": " The Latex Code for equation Compound Interestis <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>", "tag": "Economics", "prompt": "Please give me some hints on equation Compound Interest?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MFC</equation> in Factor of Production Hiring Rule is: Marginal factor cost (MFC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MFC</equation> in Factor of Production Hiring Rule?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand is: Percentage change in Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>% \\Delta P</equation> in Price Elasticity of Demand?"}
{"completion": " The equation for Calls and Puts with Different Strikes is: <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. Here is the brief introduction of Calls and Puts with Different Strikes:\n\n        Latex code for the Calls and Puts with Different Strikes. For European calls and puts, with strike prices K_{1} and K_{2}, where K_{1} < K_{2}, we know the following.\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\n            American options, For three different options with strike prices K1 < K2 < K3:\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Calls and Puts with Different Strikes?"}
{"completion": " The equation for Production Efficiency Condition is: <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. Here is the brief introduction of Production Efficiency Condition:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal Product Label\n\n\nRelated Documents\n\nProduction Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Production Efficiency Condition?"}
{"completion": " The Latex Code for equation Socially Optimal Level of Outputis <equation>\\\\text{MSB} = \\\\text{MSC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Socially Optimal Level of Output?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio is: Sharpe ratio of any asset written on a GBM.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion is: Observed stock price S(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Slope of the Total Product Curveis <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Slope of the Total Product Curve?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(t)</equation> in Monte-Carlo Simulations is: The stock price at time t, which is nearer to final stage stock price S(T).", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>S(t)</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Tax Multiplier is: <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>. Here is the brief introduction of Tax Multiplier:\n        Latex code for Tax Multiplier.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Tax Multiplier?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{MV}</equation> in Equation of Exchange is: Total spending on goods and services, measured as Monetary Value.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>\\text{MV}</equation> in Equation of Exchange?"}
{"completion": " The equation for Production Efficiency Condition is <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. The meaning of symbol <equation>MP_{L}</equation> in Production Efficiency Condition is: Marginal Product Label.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MP_{L}</equation> in Production Efficiency Condition?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>m</equation> in Compound Interest is: Number of Compounding Periods per Year.", "tag": "Economics", "prompt": "What is the meaning of <equation>m</equation> in Compound Interest?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>Q_{i}</equation> in Gini Coefficient is: The ratio of cumulative i-th group's income(increasing order)/total income.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>Q_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Autonomous Spending Multiplieris <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Autonomous Spending Multiplier?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{1}.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Total Costs is: Total Costs (TC).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{TC}</equation> in Total Costs?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Variable Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>Q</equation> in Average Variable Cost?"}
{"completion": " The Latex Code for equation Annuities Dueis <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>", "tag": "Economics", "prompt": "Can you write equation Annuities Due?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>FV</equation> in Forwards is: Future Value.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>FV</equation> in Forwards?"}
{"completion": " The equation for Put-Call Parity is: <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. Here is the brief introduction of Put-Call Parity:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. Call options give the owner the right, but not the obligation, to buy an asset at some time in the future for a predetermined strike price. Put options give the owner the right to sell. The price of calls and puts is compared in the following put-call parity formula for European options.\n        \n: Price of call option c\n: Price of put option p\n: the present value of the strike price (x), \n: \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Put-Call Parity?"}
{"completion": " The equation for Average Fixed Cost is: <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. Here is the brief introduction of Average Fixed Cost:\n        Latex code for the Allocative Average Fixed Cost. I will briefly introduce the notations in this formulation.  \n        \n: Total Fixed Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Average Fixed Cost?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>Q</equation> in Average Fixed Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>Q</equation> in Average Fixed Cost?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Total Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>Q</equation> in Average Total Cost?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MSB}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>r</equation> in Forwards is: Interest Rate.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>r</equation> in Forwards?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Simple Interest is: <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. Here is the brief introduction of Simple Interest:\n        Latex code for the Simple Interest. I will briefly introduce the notations in this formulation. \n        \n: Interest Earned\n: Principal/Present Value\n: Annual Rate\n: Time (years)\n: Future Value/Maturity Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you give me a brief introduction to Simple Interest?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates is: Forward Bond Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Marginal Cost is: <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Cost:\n        Latex code for Marginal Cost. \n        \n: Total Cost(TC)\n: Change in Total Cost(TC)\n: Quantity\n: Change in Quantity\n\n\nRelated Documents\n\nInvestopedia Marginal Cost\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Marginal Cost?"}
{"completion": " The Latex Code for equation Calls and Puts with Different Strikesis <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Annuities Dueis <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>", "tag": "Economics", "prompt": "What is the latex code of equation Annuities Due?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma is: Stochastic differential equation for X(t).", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\mathrm{d}X(t)</equation> in Ito Lemma?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>I</equation> in Simple Interest is: Interest Earned.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>I</equation> in Simple Interest?"}
{"completion": " The equation for Balanced Budget Multiplier is <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. The meaning of symbol <equation>MPC</equation> in Balanced Budget Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>MPC</equation> in Balanced Budget Multiplier?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion is: Observed stock price S(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>r</equation> in Simple Interest is: Annual Rate.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Simple Interest?"}
{"completion": " The equation for Bonds and Interest Rates is: <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. Here is the brief introduction of Bonds and Interest Rates:\n        Latex code for the Bonds and Interest Rates. The price of an s-year zero is P(0, S). The forward bond price formula  is calculated as . And the \n        non-continuous annualized rate is .\n        \n: Price of an s-year zero.\n: Forward Bond Price\n: Non-continuous annualized rate\n\n\nRelated Documents\n\nBond and Interest Rate\nUnderstanding Interest Rates, Inflation, and Bonds\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Bonds and Interest Rates?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>n</equation> in Future Value of Ordinary Annuities is: Total number of times compounded.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>n</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue is: Change in Total Revenue(TR).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{F}</equation> in Distributive Efficiency Condition is: Product of F.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Cox-Ingersoll-Ross CIRis <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Consumption Functionis <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Consumption Function?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>r</equation> in Compound Interest is: Annual Rate (decimal).", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Compound Interest?"}
{"completion": " The equation for Average Total Cost is: <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Total Cost:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n: Average Total Cost\n: Total Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Average Total Cost?"}
{"completion": " The Latex Code for equation Real Interest Rateis <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Real Interest Rate?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand is: Percentage change in quantity demanded.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Cox-Ingersoll-Ross CIRis <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Marginal Revenue Product of Labor MRPL:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Balanced Budget Multiplier is <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. The meaning of symbol <equation>MPC</equation> in Balanced Budget Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>MPC</equation> in Balanced Budget Multiplier?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion SDEs is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>U</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Balanced Budget Multiplier is <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. The meaning of symbol <equation>MPC</equation> in Balanced Budget Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>MPC</equation> in Balanced Budget Multiplier?"}
{"completion": " The related materials of Investment is: 1.Principles Economics:<url>https://open.lib.umn.edu/principleseconomics/chapter/28-2-the-aggregate-expenditures-model/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Investment?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity is: the present value of the strike price (x),.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity?"}
{"completion": " The Latex Code for equation Production Efficiency Conditionis <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Production Efficiency Condition?"}
{"completion": " The equation for Distributive Efficiency Condition is: <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. Here is the brief introduction of Distributive Efficiency Condition:\n        Latex code for Distributive Efficiency Condition. I will briefly introduce the notations in this formulation. Distributive efficiency is concerned with an equitable distribution of resources because of the law of diminishing marginal returns. The Law of diminishing marginal returns states that as consumption of a good increase we tend to get diminishing marginal utility. \n        \n: Marginal Utility of F\n: Product of F\n: Marginal Utility of C\n: Product of C\n\n\nRelated Documents\n\nDistributive Efficiency Definition\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Distributive Efficiency Condition?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>P</equation> in Simple Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Simple Interest?"}
{"completion": " The Latex Code for equation Optimal Combination of Resources Conditionis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Optimal Combination of Resources Condition?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Total Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>Q</equation> in Average Total Cost?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>i</equation> in Future Value of Ordinary Annuities is: Rate per period.", "tag": "Economics", "prompt": "What does the symbol mean <equation>i</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Average Fixed Costis <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Average Fixed Cost?"}
{"completion": " The Latex Code for equation Marginal Revenue Product of Labor MRPLis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections is: Government Spending.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>\\text{G}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>Q</equation> in Average Fixed Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>Q</equation> in Average Fixed Cost?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>TFC</equation> in Average Fixed Cost is: Total Fixed Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>TFC</equation> in Average Fixed Cost?"}
{"completion": " The Latex Code for equation Future Value of Ordinary Annuitiesis <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>", "tag": "Economics", "prompt": "Please give me some hints on equation Future Value of Ordinary Annuities?"}
{"completion": " The equation for Put-Call Parity is: <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. Here is the brief introduction of Put-Call Parity:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. Call options give the owner the right, but not the obligation, to buy an asset at some time in the future for a predetermined strike price. Put options give the owner the right to sell. The price of calls and puts is compared in the following put-call parity formula for European options.\n        \n: Price of call option c\n: Price of put option p\n: the present value of the strike price (x), \n: \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Put-Call Parity?"}
{"completion": " The equation for Geometric Brownian Motion is: <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. Here is the brief introduction of Geometric Brownian Motion:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Geometric Brownian Motion?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPC</equation> in Autonomous Spending Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>MPC</equation> in Autonomous Spending Multiplier?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSB</equation> in Allocative Efficiency Condition is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MSB</equation> in Allocative Efficiency Condition?"}
{"completion": " The Latex Code for equation Effective Rateis <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>", "tag": "Economics", "prompt": "Can you write equation Effective Rate?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\sigma</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>i</equation> in Future Value of Ordinary Annuities is: Rate per period.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>i</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Tax Multiplieris <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Tax Multiplier?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>TP</equation> in Average Product is: Total Product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>TP</equation> in Average Product?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\mu</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(0, S)</equation> in Bonds and Interest Rates is: Price of an s-year zero..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P(0, S)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{F}</equation> in Distributive Efficiency Condition is: Product of F.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>A(T)</equation> in Asian Options is: Arithmetic average of option price at time T.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>A(T)</equation> in Asian Options?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded continuously..", "tag": "Economics", "prompt": "What is the meaning of <equation>r_{e} = e^{r} - 1</equation> in Effective Rate?"}
{"completion": " The Latex Code for equation Average Total Costis <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Average Total Cost?"}
{"completion": " The equation for Real Interest Rate is: <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Real Interest Rate:\n        Latex code for Real Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Real Interest Rate?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>MU</equation> in Optimal Consumption Rule is: Marginal utility (MU).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MU</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>Q_{i}</equation> in Gini Coefficient is: The ratio of cumulative i-th group's income(increasing order)/total income.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>Q_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>n</equation> in Present Value of Ordinary Annuities is: Total number of times compounded, n=mt.", "tag": "Economics", "prompt": "What is the meaning of <equation>n</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TFC}</equation> in Total Costs is: Total Fixed Costs (TFC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{TFC}</equation> in Total Costs?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPS</equation> in Autonomous Spending Multiplier is: Marginal Propensity Save.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>MPS</equation> in Autonomous Spending Multiplier?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>AP</equation> in Average Product is: Average Product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>AP</equation> in Average Product?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TR}</equation> in Profit is: Total Revenue.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{TR}</equation> in Profit?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(t)</equation> in Monte-Carlo Simulations is: The stock price at time t, which is nearer to final stage stock price S(T).", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>S(t)</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC is: Marginal Factor Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>r</equation> in Simple Interest is: Annual Rate.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>r</equation> in Simple Interest?"}
{"completion": " The related materials of Early Exercise for American Options is: 1.Investopedia Put Call Parity:<url>https://www.investopedia.com/terms/p/putcallparity.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Early Exercise for American Options?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{U}</equation> in Investment is: Unplanned investment.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>I_{U}</equation> in Investment?"}
{"completion": " The Latex Code for equation Black-Derman-Toy BDTis <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Black-Derman-Toy BDT?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>P_{i}</equation> in Gini Coefficient is: The ratio of i-th group's population(P)/total population(P).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Calls and Puts Arbitrageis <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Calls and Puts Arbitrage?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity is: the present value of the strike price (x),.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity?"}
{"completion": " The related materials of Optimal Combination of Resources Condition is: 1.How Is the Marginal Product of Labor Determined:<url>https://www.masterclass.com/articles/learn-about-marginal-product-of-labor-in-economics</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Optimal Combination of Resources Condition?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TVC}</equation> in Total Costs is: Total Variable Costs (TVC).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{TVC}</equation> in Total Costs?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of put option p.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>F_{t,T}(S)</equation> in Forwards is: Forward Contract at strike price S.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>F_{t,T}(S)</equation> in Forwards?"}
{"completion": " The equation for Standard Brownian Motion is: <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. Here is the brief introduction of Standard Brownian Motion:\n        Latex code for the Standard Brownian Motion. I will briefly introduce the notations in this formulation. {Z(t)} has independent increments, and {Z(t)} has stationary increments such that Z (t + s) ? Z (t) follows standard normal distribution\n        \n: Value of Z at time stamp t\n: Stationary increments of Standard Brownian Motion\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Standard Brownian Motion?"}
{"completion": " The equation for Optimal Combination of Resources Condition is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Optimal Combination of Resources Condition:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Optimal Combination of Resources Condition?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{PQ}</equation> in Equation of Exchange is: Total spending on goods and services, measured as PY (or nominal GDP).", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>\\text{PQ}</equation> in Equation of Exchange?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts is: Payoff a power contract at time T.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>S^{a}(T)</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL is: Price.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The related materials of Price for a Competitive Firm is: 1.Investopedia Price Elasticity of Demand:<url>https://www.investopedia.com/terms/p/priceelasticity.asp</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Price for a Competitive Firm?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is: <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. Here is the brief introduction of Cox-Ingersoll-Ross CIR:\n        Latex code for the Cox-Ingersoll-Ross model. \n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nCox-Ingersoll-Ross Model\nA THEORY OF THE TERM STRUCTURE OF INTEREST RATES\nCox-Ingersoll-Ross (CIR) model-Mathworks\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Average Productis <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Average Product?"}
{"completion": " The equation for Tax Multiplier is: <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>. Here is the brief introduction of Tax Multiplier:\n        Latex code for Tax Multiplier.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Tax Multiplier?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion is: Stationary increments of Standard Brownian Motion.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The Latex Code for equation Merchandise Trade Balanceis <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Merchandise Trade Balance?"}
{"completion": " The equation for Gini Coefficient is: <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. Here is the brief introduction of Gini Coefficient:\n        Latex code for Gini Coefficient.  The Gini coefficient (Gini index or Gini ratio) is a statistical measure of economic inequality in a population. The coefficient measures the dispersion of income or distribution of wealth among the members of a population.\n        \n: Area between Line of Perfect Equality and Lorenz Curve.\n: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income).\n: The ratio of i-th group's income/total income\n: The ratio of cumulative i-th group's income(increasing order)/total income\n: The ratio of i-th group's population(P)/total population(P)\n\n\nRelated Documents\n\nCorporate Finance Institute Gini-coefficient\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Gini Coefficient?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC is: Change in total cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>TC</equation> in Marginal Cost is: Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>TC</equation> in Marginal Cost?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Variable Cost is: Total Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>TC</equation> in Average Variable Cost?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPC</equation> in Autonomous Spending Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>MPC</equation> in Autonomous Spending Multiplier?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MSC}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections is: Government Spending.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>r</equation> in Compound Interest is: Annual Rate (decimal).", "tag": "Economics", "prompt": "What is the meaning of <equation>r</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Average Revenueis <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Average Revenue?"}
{"completion": " The Latex Code for equation Balanced Budget Multiplieris <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Balanced Budget Multiplier?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>AVC</equation> in Average Variable Cost is: Average Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>AVC</equation> in Average Variable Cost?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>P</equation> in Optimal Consumption Rule is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost is: Change in Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections is: Exports.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Ito Lemma is: <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. Here is the brief introduction of Ito Lemma:\n        Latex code for the Ito Lemma.\n        \n: Diffusion\n: Stochastic differential equation for X(t)\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Ito Lemma?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options is: put protection if the stock price should fall..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{B}</equation> in Gini Coefficient is: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income)..", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>S_{B}</equation> in Gini Coefficient?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage is: Strike price of option 3.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>K_{3}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Investmentis <equation>I=I_{P}+I_{U}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Investment?"}
{"completion": " The equation for Banks Reserve Ratio is: <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>. Here is the brief introduction of Banks Reserve Ratio:\n        Latex code for the Banks Reserve Ratio.\n        \n \n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Banks Reserve Ratiois <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Banks Reserve Ratio?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>AP</equation> in Average Product is: Average Product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>AP</equation> in Average Product?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>G(T)</equation> in Asian Options is: Geometric average of option price at time T.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>G(T)</equation> in Asian Options?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Variable Cost is: Total Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>TC</equation> in Average Variable Cost?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>P</equation> in Compound Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Allocative Efficiency Conditionis <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Allocative Efficiency Condition?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Unemployment Rate is: <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>. Here is the brief introduction of Unemployment Rate:\n        Latex code for Unemployment Rate.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Unemployment Rate?"}
{"completion": " The equation for Autonomous Spending Multiplier is: <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. Here is the brief introduction of Autonomous Spending Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n: Marginal Propensity Save\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Autonomous Spending Multiplier?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity is: the present value of the strike price (x),.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>A</equation> in Simple Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "What is the meaning of <equation>A</equation> in Simple Interest?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections is: Government Spending.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>\\text{G}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL is: Price.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Forwards is: <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. Here is the brief introduction of Forwards:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. A forward contract is an agreement in which the buyer agrees at time t to pay the seller at time T and receive the asset at time T.\n        \n: Forward Contract at strike price S\n: Interest Rate\n: Future Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Forwards?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>r</equation> in Simple Interest is: Annual Rate.", "tag": "Economics", "prompt": "What does the symbol mean <equation>r</equation> in Simple Interest?"}
{"completion": " The Latex Code for equation Elasticity of Supplyis <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Elasticity of Supply?"}
{"completion": " The equation for Equation of Exchange is: <equation>\\\\text{MV} = \\\\text{PQ}</equation>. Here is the brief introduction of Equation of Exchange:\n        Latex code for Equation of Exchange. The equation of exchange says simply that total spending on goods and services, measured as MV, equals total spending on goods and services, measured as PY (or nominal GDP). The equation of exchange is thus an identity, a mathematical expression that is true by definition.\n        \n: Total spending on goods and services, measured as Monetary Value\n: Total spending on goods and services, measured as PY (or nominal GDP)\n\n\nRelated Documents\n\nInvestopedia: equation of exchange\nMonetary Policy and the Equation of Exchange\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Equation of Exchange?"}
{"completion": " The Latex Code for equation Banks Reserve Ratiois <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Autonomous Spending Multiplieris <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Autonomous Spending Multiplier?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Merchandise Trade Balanceis <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Merchandise Trade Balance?"}
{"completion": " The equation for Average Product is: <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. Here is the brief introduction of Average Product:\n        Latex code for the Average Product. I will briefly introduce the notations in this formulation.  \n        \n: Average Product\n: Total Product\n: Quantity of Input\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Average Product?"}
{"completion": " The equation for Autonomous Spending Multiplier is: <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. Here is the brief introduction of Autonomous Spending Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n: Marginal Propensity Save\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Autonomous Spending Multiplier?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\delta</equation> in Sharpe Ratio is: Compounded Dividend Rate.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\delta</equation> in Sharpe Ratio?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>R</equation> in Present Value of Ordinary Annuities is: Payment made in each period.", "tag": "Economics", "prompt": "What does the symbol mean <equation>R</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Marginal Costis <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Marginal Cost?"}
{"completion": " The Latex Code for equation Distributive Efficiency Conditionis <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Marginal Product of Laboris <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Marginal Product of Labor?"}
{"completion": " The equation for Cross-Price Elasticity of Demand is: <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>. Here is the brief introduction of Cross-Price Elasticity of Demand:\n        Latex code for Cross-Price Elasticity of Demand. I will briefly introduce the notations in this formulation.  \n        \n\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>P</equation> in Simple Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Simple Interest?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Tax Multiplier is: <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>. Here is the brief introduction of Tax Multiplier:\n        Latex code for Tax Multiplier.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Tax Multiplier?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPS</equation> in Autonomous Spending Multiplier is: Marginal Propensity Save.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>MPS</equation> in Autonomous Spending Multiplier?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Optimal Combination of Resources Condition is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>A(T)</equation> in Asian Options is: Arithmetic average of option price at time T.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>A(T)</equation> in Asian Options?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>R_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue Product is: Marginal Revenue(MR).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MR</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>A</equation> in Simple Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>A</equation> in Simple Interest?"}
{"completion": " The Latex Code for equation Marginal Revenueis <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Marginal Revenue?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>P</equation> in Price for a Competitive Firm is: Price.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Price for a Competitive Firm?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Total Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>Q</equation> in Average Total Cost?"}
{"completion": " The Latex Code for equation Early Exercise for American Optionsis <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Early Exercise for American Options?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>R</equation> in Present Value of Ordinary Annuities is: Payment made in each period.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>R</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Calls and Puts with Different Strikes is: <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. Here is the brief introduction of Calls and Puts with Different Strikes:\n\n        Latex code for the Calls and Puts with Different Strikes. For European calls and puts, with strike prices K_{1} and K_{2}, where K_{1} < K_{2}, we know the following.\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\n            American options, For three different options with strike prices K1 < K2 < K3:\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Calls and Puts with Different Strikes?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>ATC</equation> in Average Total Cost is: Average Total Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>ATC</equation> in Average Total Cost?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates is: Forward Bond Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Total Costs is: Total Costs (TC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{TC}</equation> in Total Costs?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC is: Marginal Factor Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Total Costs is: Total Costs (TC).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{TC}</equation> in Total Costs?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{1}.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates is: Non-continuous annualized rate.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level is: Marginal Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t)</equation> in Standard Brownian Motion is: Value of Z at time stamp t.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The Latex Code for equation Factor of Production Hiring Ruleis <equation>\\\\text{MRP} = \\\\text{MFC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Factor of Production Hiring Rule?"}
{"completion": " The equation for Marginal Revenue Product is: <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. Here is the brief introduction of Marginal Revenue Product:\n        Latex code for Marginal Revenue Product. The amount that an additional unit of a factor adds to a firm's total revenue during a period is called the marginal revenue product (MRP) of the factor. An additional unit of a factor of production adds to a firm\u2019s revenue in a two-step process: first, it increases the firm's output. Second, the increased output increases the firm\u2019s total revenue. We find marginal revenue product by multiplying the marginal product (MP) of the factor by the marginal revenue (MR). I will briefly introduce the notations in this formulation.  \n        \n: Marginal Product(MP)\n: Marginal Revenue(MR)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Marginal Revenue Product?"}
{"completion": " The equation for Marginal Cost is: <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Cost:\n        Latex code for Marginal Cost. \n        \n: Total Cost(TC)\n: Change in Total Cost(TC)\n: Quantity\n: Change in Quantity\n\n\nRelated Documents\n\nInvestopedia Marginal Cost\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Marginal Cost?"}
{"completion": " The Latex Code for equation Investmentis <equation>I=I_{P}+I_{U}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Investment?"}
{"completion": " The equation for Early Exercise for American Options is: <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. Here is the brief introduction of Early Exercise for American Options:\n\n            So we exercise the call option if the pros are greater than the cons, specifically, we exercise if:\n        \n\n: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons. \n: Early Exercise getting the stock's dividend payments\n: Pay the strike earlier and therefore miss the interest on that money\n: put protection if the stock price should fall.\n: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise. \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Early Exercise for American Options?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>W_{i}</equation> in Gini Coefficient is: The ratio of i-th group's income/total income.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>W_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Consumer Price Index CPIis <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Consumer Price Index CPI?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve is: Change in Total Product.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{MV}</equation> in Equation of Exchange is: Total spending on goods and services, measured as Monetary Value.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MV}</equation> in Equation of Exchange?"}
{"completion": " The Latex Code for equation Sharpe Ratiois <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Sharpe Ratio?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSB</equation> in Allocative Efficiency Condition is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MSB</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Price for a Competitive Firm is: <equation>P = MR</equation>. Here is the brief introduction of Price for a Competitive Firm:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal revenue (MR)\n: Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Price for a Competitive Firm?"}
{"completion": " The Latex Code for equation Asian Optionsis <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Asian Options?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: Pay the strike earlier and therefore miss the interest on that money.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Elasticity of Supplyis <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Elasticity of Supply?"}
{"completion": " The Latex Code for equation Production Efficiency Conditionis <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Production Efficiency Condition?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>R</equation> in Future Value of Ordinary Annuities is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>R</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPC</equation> in Autonomous Spending Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>MPC</equation> in Autonomous Spending Multiplier?"}
{"completion": " The related materials of Factor of Production Hiring Rule is: 1.The Demand for Labor:<url>https://open.lib.umn.edu/principleseconomics/chapter/12-1-the-demand-for-labor/</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Factor of Production Hiring Rule?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage is: Strike price of option 1.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Distributive Efficiency Condition is: <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. Here is the brief introduction of Distributive Efficiency Condition:\n        Latex code for Distributive Efficiency Condition. I will briefly introduce the notations in this formulation. Distributive efficiency is concerned with an equitable distribution of resources because of the law of diminishing marginal returns. The Law of diminishing marginal returns states that as consumption of a good increase we tend to get diminishing marginal utility. \n        \n: Marginal Utility of F\n: Product of F\n: Marginal Utility of C\n: Product of C\n\n\nRelated Documents\n\nDistributive Efficiency Definition\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Unemployment Rateis <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Unemployment Rate?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is: <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. Here is the brief introduction of Geometric Brownian Motion SDEs:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t)</equation> in Standard Brownian Motion is: Value of Z at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Production Efficiency Condition is: <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. Here is the brief introduction of Production Efficiency Condition:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal Product Label\n\n\nRelated Documents\n\nProduction Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Production Efficiency Condition?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Present Value of Ordinary Annuitiesis <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>", "tag": "Economics", "prompt": "Please give me some hints on equation Present Value of Ordinary Annuities?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>S</equation> in Annuities Due is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>S</equation> in Annuities Due?"}
{"completion": " The Latex Code for equation Elasticity of Supplyis <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Elasticity of Supply?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Annuities Dueis <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>", "tag": "Economics", "prompt": "What is the equation of Annuities Due?"}
{"completion": " The Latex Code for equation Stock Prices as Geometric Brownian Motionis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Compound Interest is: <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. Here is the brief introduction of Compound Interest:\n        Latex code for the Compound Interest. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Maturity Value\n: Principal/Present Value\n: Annual Rate (decimal)\n: Number of Compounding Periods per Year\n: Time (years)\n: Loan/investment is compounded continuously\n\n\nRelated Documents\n\nCompound Interest Calculator\nInvestopedia Compound Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Please give me detailed tutorial of Compound Interest?"}
{"completion": " The Latex Code for equation Marginal Revenue Productis <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Marginal Revenue Product?"}
{"completion": " The equation for Bonds and Interest Rates is: <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. Here is the brief introduction of Bonds and Interest Rates:\n        Latex code for the Bonds and Interest Rates. The price of an s-year zero is P(0, S). The forward bond price formula  is calculated as . And the \n        non-continuous annualized rate is .\n        \n: Price of an s-year zero.\n: Forward Bond Price\n: Non-continuous annualized rate\n\n\nRelated Documents\n\nBond and Interest Rate\nUnderstanding Interest Rates, Inflation, and Bonds\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Bonds and Interest Rates?"}
{"completion": " The equation for Varying Times to Expiration is: <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. Here is the brief introduction of Varying Times to Expiration:\n\n            For American options, when expiration T2 > T1, the above equations holds.\n        \n\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Varying Times to Expiration?"}
{"completion": " The equation for Elasticity of Supply is: <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>. Here is the brief introduction of Elasticity of Supply:\n        Latex code for Elasticity of Supply. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Elasticity of Supply?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>AVC</equation> in Average Variable Cost is: Average Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>AVC</equation> in Average Variable Cost?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPC</equation> in Autonomous Spending Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>MPC</equation> in Autonomous Spending Multiplier?"}
{"completion": " The Latex Code for equation Standard Brownian Motionis <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Standard Brownian Motion?"}
{"completion": " The Latex Code for equation Average Variable Costis <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Average Variable Cost?"}
{"completion": " The related materials of Geometric Brownian Motion SDEs is: 1.Geometric Brownian Motion:<url>https://www.quantstart.com/articles/Geometric-Brownian-Motion/</url>;2.Geometric Brownian motion:<url>http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GBM.pdf</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Annuities Due is: <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. Here is the brief introduction of Annuities Due:\n        Latex code for the Future Value of Annuities Due. I will briefly introduce the notations in this formulation. \n        The payment/deposit is at the BEGINNING of the period\n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "I am interested in Annuities Due?"}
{"completion": " The equation for Optimal Consumption Rule is: <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. Here is the brief introduction of Optimal Consumption Rule:\n        Latex code for Optimal Consumption Rule. \n        \n: Marginal utility (MU)\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Optimal Consumption Rule?"}
{"completion": " The Latex Code for equation Average Variable Costis <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Average Variable Cost?"}
{"completion": " The equation for Socially Optimal Level of Output is: <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. Here is the brief introduction of Socially Optimal Level of Output:\n        Latex code for Socially Optimal Level of Output.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Socially Optimal Level of Output?"}
{"completion": " The Latex Code for equation Put-Call Parityis <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Put-Call Parity?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Put-Call Parity is: <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. Here is the brief introduction of Put-Call Parity:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. Call options give the owner the right, but not the obligation, to buy an asset at some time in the future for a predetermined strike price. Put options give the owner the right to sell. The price of calls and puts is compared in the following put-call parity formula for European options.\n        \n: Price of call option c\n: Price of put option p\n: the present value of the strike price (x), \n: \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Put-Call Parity?"}
{"completion": " The equation for Monte-Carlo Simulations is: <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. Here is the brief introduction of Monte-Carlo Simulations:\n        Latex code for the Monte-Carlo Simulations of stock prices. I will briefly introduce the notations in this formulation. Monte-Carlo simulation simulates stock prices, calculate the payoff the option for each of those simulated prices, find the average payoff, and then discount the average payoff. Firstly, we start with iid uniform numbers u_{1} to u_{n}, calculate standard normal variable z_{i} as , convert to normal variable .  The variance of the Monte-Carlo estimate is calculated as . \n        \n: The stock price at time T\n: The stock price at time t, which is nearer to final stage stock price S(T)\n: The i-th simulated payoff\n: The variance of stock price\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Monte-Carlo Simulations?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: Pay the strike earlier and therefore miss the interest on that money.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Black-Derman-Toy BDTis <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Black-Derman-Toy BDT?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Variable Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>Q</equation> in Average Variable Cost?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. Here is the brief introduction of Risk-Neutral Valuation and Power Contracts:\n        Latex code for Risk-Neutral Valuation and Power Contracts.\n        \n: Payoff a power contract at time T\n: Price of the power contract\n: Risk-neutral equations\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Marginal Revenue Product of Labor MRPL:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Marginal Costis <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Marginal Cost?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio is: Sharpe ratio of any asset written on a GBM.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio?"}
{"completion": " The Latex Code for equation Optimal Combination of Resources Conditionis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Optimal Combination of Resources Condition?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(t)</equation> in Monte-Carlo Simulations is: The stock price at time t, which is nearer to final stage stock price S(T).", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>S(t)</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Distributive Efficiency Conditionis <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Distributive Efficiency Condition?"}
{"completion": " The equation for Effective Rate is: <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. Here is the brief introduction of Effective Rate:\n        Latex code for the Effective Rate. I will briefly introduce the notations in this formulation. \n        \n: Effective Rate\n: Compute the effective rate if your loan/investment is compounded m times per year.\n: Compute the effective rate if your loan/investment is compounded continuously.\n\n\nRelated Documents\n\nInvestopedia Effective Rate\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "I am interested in Effective Rate?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A = Pe^{rt}</equation> in Compound Interest is: Loan/investment is compounded continuously.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>A = Pe^{rt}</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Marginal Product of Laboris <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Marginal Product of Labor?"}
{"completion": " The related materials of Gini Coefficient is: 1.Corporate Finance Institute Gini-coefficient:<url>https://corporatefinanceinstitute.com/resources/economics/gini-coefficient/</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Gini Coefficient?"}
{"completion": " The Latex Code for equation Marginal Revenue Product of Labor MRPLis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Simple Interest is: <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. Here is the brief introduction of Simple Interest:\n        Latex code for the Simple Interest. I will briefly introduce the notations in this formulation. \n        \n: Interest Earned\n: Principal/Present Value\n: Annual Rate\n: Time (years)\n: Future Value/Maturity Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Please give me detailed tutorial of Simple Interest?"}
{"completion": " The Latex Code for equation Banks Reserve Ratiois <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Banks Reserve Ratio?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC is: Marginal Factor Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Price for a Competitive Firm is: <equation>P = MR</equation>. Here is the brief introduction of Price for a Competitive Firm:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal revenue (MR)\n: Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Price for a Competitive Firm?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand is: Percentage change in quantity demanded.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of put option p.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>MR</equation> in Price for a Competitive Firm is: Marginal revenue (MR).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MR</equation> in Price for a Competitive Firm?"}
{"completion": " The Latex Code for equation Future Value of Ordinary Annuitiesis <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>", "tag": "Economics", "prompt": "Show me the latex code of equation Future Value of Ordinary Annuities?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{MV}</equation> in Equation of Exchange is: Total spending on goods and services, measured as Monetary Value.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>\\text{MV}</equation> in Equation of Exchange?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A</equation> in Compound Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>A</equation> in Compound Interest?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections is: Exports.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>MR</equation> in Price for a Competitive Firm is: Marginal revenue (MR).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MR</equation> in Price for a Competitive Firm?"}
{"completion": " The Latex Code for equation Put-Call Parityis <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Put-Call Parity?"}
{"completion": " The Latex Code for equation Average Productis <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Average Product?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>X</equation> in Ito Lemma is: Diffusion.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>X</equation> in Ito Lemma?"}
{"completion": " The Latex Code for equation Price for a Competitive Firmis <equation>P = MR</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Price for a Competitive Firm?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: Pay the strike earlier and therefore miss the interest on that money.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{2}.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Investmentis <equation>I=I_{P}+I_{U}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Investment?"}
{"completion": " The equation for Autonomous Spending Multiplier is: <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. Here is the brief introduction of Autonomous Spending Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n: Marginal Propensity Save\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Autonomous Spending Multiplier?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>G(T)</equation> in Asian Options is: Geometric average of option price at time T.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>G(T)</equation> in Asian Options?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma is: Stochastic differential equation for X(t).", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\mathrm{d}X(t)</equation> in Ito Lemma?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>F_{t,T}(S)</equation> in Forwards is: Forward Contract at strike price S.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>F_{t,T}(S)</equation> in Forwards?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>QI</equation> in Average Product is: Quantity of Input.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>QI</equation> in Average Product?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{C}</equation> in Distributive Efficiency Condition is: Product of C.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Allocative Efficiency Condition is: <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. Here is the brief introduction of Allocative Efficiency Condition:\n        Latex code for the Allocative Efficiency Condition. I will briefly introduce the notations in this formulation.  \n        Allocative efficiency occurs when consumer demand is completely met by supply. In other words, businesses are providing the exact supply that consumers want.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\nAllocative Efficiency: Definition, Example Productive Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Allocative Efficiency Condition?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>TP</equation> in Average Product is: Total Product.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>TP</equation> in Average Product?"}
{"completion": " The equation for Forwards is: <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. Here is the brief introduction of Forwards:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. A forward contract is an agreement in which the buyer agrees at time t to pay the seller at time T and receive the asset at time T.\n        \n: Forward Contract at strike price S\n: Interest Rate\n: Future Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Forwards?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs is: Volatility.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\sigma</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Gross Domestic Product Deflatoris <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Gross Domestic Product Deflator?"}
{"completion": " The Latex Code for equation Geometric Brownian Motionis <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Profitis <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Profit?"}
{"completion": " The equation for Geometric Brownian Motion is: <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. Here is the brief introduction of Geometric Brownian Motion:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Geometric Brownian Motion?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue Product is: Marginal Revenue(MR).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MR</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>R</equation> in Present Value of Ordinary Annuities is: Payment made in each period.", "tag": "Economics", "prompt": "What is the meaning of <equation>R</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Average Total Cost is: <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Total Cost:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n: Average Total Cost\n: Total Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Average Total Cost?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>Y(t)</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Profit is: <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. Here is the brief introduction of Profit:\n        Latex code for Price for a Competitive Firm.\n        \n: Total Revenue\n: Total Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Profit?"}
{"completion": " The equation for Marginal Revenue is: <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Revenue:\n        Latex code for Marginal Revenue. \n        \n: Marginal Revenue\n: Change in Total Revenue(TR)\n: Change in Quantity(Q)\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Marginal Revenue?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>MPL</equation> in Marginal Product of Labor is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MPL</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Average Revenueis <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Average Revenue?"}
{"completion": " The equation for Optimal Consumption Rule is: <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. Here is the brief introduction of Optimal Consumption Rule:\n        Latex code for Optimal Consumption Rule. \n        \n: Marginal utility (MU)\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Optimal Consumption Rule?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>I</equation> in Simple Interest is: Interest Earned.", "tag": "Economics", "prompt": "What is the meaning of <equation>I</equation> in Simple Interest?"}
{"completion": " The Latex Code for equation Gini Coefficientis <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Gini Coefficient?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Put Option Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Socially Optimal Level of Output is: <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. Here is the brief introduction of Socially Optimal Level of Output:\n        Latex code for Socially Optimal Level of Output.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Socially Optimal Level of Output?"}
{"completion": " The equation for Equality of Leakages and Injections is: <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. Here is the brief introduction of Equality of Leakages and Injections:\n        Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy \u00e2\u20ac\u201c that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.\n        \n: Investment\n: Government Spending\n: Exports\n\n\nRelated Documents\n\nWhy are leakages equal to injections?\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Equality of Leakages and Injections?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Total Costs is: Total Costs (TC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{TC}</equation> in Total Costs?"}
{"completion": " The Latex Code for equation Simple Interestis <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>", "tag": "Economics", "prompt": "Please give me some hints on equation Simple Interest?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition is: Marginal Utility of C.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is: <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. Here is the brief introduction of Cox-Ingersoll-Ross CIR:\n        Latex code for the Cox-Ingersoll-Ross model. \n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nCox-Ingersoll-Ross Model\nA THEORY OF THE TERM STRUCTURE OF INTEREST RATES\nCox-Ingersoll-Ross (CIR) model-Mathworks\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Cross-Price Elasticity of Demand is: <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>. Here is the brief introduction of Cross-Price Elasticity of Demand:\n        Latex code for Cross-Price Elasticity of Demand. I will briefly introduce the notations in this formulation.  \n        \n\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(T)</equation> in Monte-Carlo Simulations is: The stock price at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>S(T)</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Equation of Exchangeis <equation>\\\\text{MV} = \\\\text{PQ}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Equation of Exchange?"}
{"completion": " The Latex Code for equation Calls and Puts Arbitrageis <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Calls and Puts Arbitrage?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Tax Multiplieris <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Tax Multiplier?"}
{"completion": " The Latex Code for equation Calls and Puts with Different Strikesis <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Calls and Puts Arbitrageis <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Average Fixed Costis <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Average Fixed Cost?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>n</equation> in Annuities Due is: Total number of times compounded.", "tag": "Economics", "prompt": "What is the meaning of <equation>n</equation> in Annuities Due?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition is: Marginal Utility of F.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>R_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Average Fixed Cost is: <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. Here is the brief introduction of Average Fixed Cost:\n        Latex code for the Allocative Average Fixed Cost. I will briefly introduce the notations in this formulation.  \n        \n: Total Fixed Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Average Fixed Cost?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>r</equation> in Forwards is: Interest Rate.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>r</equation> in Forwards?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{P}</equation> in Investment is: Planned investment.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>I_{P}</equation> in Investment?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of put option p.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Marginal Factor Cost MFC is: <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. Here is the brief introduction of Marginal Factor Cost MFC:\n        Latex code for Marginal Revenue Product of Labor MRPL. Marginal factor cost (MFC) is the change in total cost (\\Delta \\text{TC}}) divided by the change in the quantity of the factor:\n        \n: Marginal Factor Cost\n: Change in total cost\n: Change in the quantity of the factor\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Marginal Factor Cost MFC?"}
{"completion": " The equation for Average Revenue is: <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>. Here is the brief introduction of Average Revenue:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Average Revenue?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>W_{i}</equation> in Gini Coefficient is: The ratio of i-th group's income/total income.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>W_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC is: Change in total cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage is: Strike price of option 2.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{P}</equation> in Investment is: Planned investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>I_{P}</equation> in Investment?"}
{"completion": " The equation for Varying Times to Expiration is: <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. Here is the brief introduction of Varying Times to Expiration:\n\n            For American options, when expiration T2 > T1, the above equations holds.\n        \n\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Varying Times to Expiration?"}
{"completion": " The equation for Monte-Carlo Simulations is: <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. Here is the brief introduction of Monte-Carlo Simulations:\n        Latex code for the Monte-Carlo Simulations of stock prices. I will briefly introduce the notations in this formulation. Monte-Carlo simulation simulates stock prices, calculate the payoff the option for each of those simulated prices, find the average payoff, and then discount the average payoff. Firstly, we start with iid uniform numbers u_{1} to u_{n}, calculate standard normal variable z_{i} as , convert to normal variable .  The variance of the Monte-Carlo estimate is calculated as . \n        \n: The stock price at time T\n: The stock price at time t, which is nearer to final stage stock price S(T)\n: The i-th simulated payoff\n: The variance of stock price\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Balanced Budget Multiplieris <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Balanced Budget Multiplier?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition is: Marginal Utility of C.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs is: Volatility.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Ito Lemmais <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Ito Lemma?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations is: The variance of stock price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Early Exercise for American Options is: <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. Here is the brief introduction of Early Exercise for American Options:\n\n            So we exercise the call option if the pros are greater than the cons, specifically, we exercise if:\n        \n\n: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons. \n: Early Exercise getting the stock's dividend payments\n: Pay the strike earlier and therefore miss the interest on that money\n: put protection if the stock price should fall.\n: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise. \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Early Exercise for American Options?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\mu</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Price for a Competitive Firmis <equation>P = MR</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Price for a Competitive Firm?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Variable Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>Q</equation> in Average Variable Cost?"}
{"completion": " The related materials of Annuities Due is: 1.Ordinary Annuity:<url>https://www.investopedia.com/terms/o/ordinaryannuity.asp</url>;", "tag": "Economics", "prompt": "Can you help me find related materials of Annuities Due?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>TFC</equation> in Average Fixed Cost is: Total Fixed Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>TFC</equation> in Average Fixed Cost?"}
{"completion": " The Latex Code for equation Equality of Leakages and Injectionsis <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Equality of Leakages and Injections?"}
{"completion": " The equation for Average Fixed Cost is: <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. Here is the brief introduction of Average Fixed Cost:\n        Latex code for the Allocative Average Fixed Cost. I will briefly introduce the notations in this formulation.  \n        \n: Total Fixed Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Average Fixed Cost?"}
{"completion": " The Latex Code for equation Banks Reserve Ratiois <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Banks Reserve Ratio?"}
{"completion": " The related materials of Cross-Price Elasticity of Demand is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSB</equation> in Allocative Efficiency Condition is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MSB</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Autonomous Spending Multiplier is: <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. Here is the brief introduction of Autonomous Spending Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n: Marginal Propensity Save\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Autonomous Spending Multiplier?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC is: Change in total cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The Latex Code for equation Risk-Neutral Valuation and Power Contractsis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded continuously..", "tag": "Economics", "prompt": "Can you explain the symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Calls and Puts Arbitrage is: <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. Here is the brief introduction of Calls and Puts Arbitrage:\n\n        Latex code for the Calls and Puts Arbitrage. Three different options have strike prices K1, K2, K3 and K1 < K2 < K3 holds.\n        An important formula for determining arbitrage opportunities comes from the following equations.\n        \n\n: Strike price of option 1\n: Strike price of option 2\n: Strike price of option 3\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Calls and Puts Arbitrage?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue is: Change in Total Revenue(TR).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{TR}</equation> in Marginal Revenue?"}
{"completion": " The related materials of Unemployment Rate is: 1.Merchandise imports:<url>https://data.worldbank.org/indicator/TM.VAL.MRCH.CD.WT</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Unemployment Rate?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>R</equation> in Present Value of Ordinary Annuities is: Payment made in each period.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>R</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Profit is: <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. Here is the brief introduction of Profit:\n        Latex code for Price for a Competitive Firm.\n        \n: Total Revenue\n: Total Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Profit?"}
{"completion": " The equation for Cross-Price Elasticity of Demand is: <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>. Here is the brief introduction of Cross-Price Elasticity of Demand:\n        Latex code for Cross-Price Elasticity of Demand. I will briefly introduce the notations in this formulation.  \n        \n\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Profit-Maximizing Output Level is: <equation>MR = MC</equation>. Here is the brief introduction of Profit-Maximizing Output Level:\n        Latex code for Profit-Maximizing Output Level.\n        \n: Marginal Revenue\n: Marginal Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Profit-Maximizing Output Level?"}
{"completion": " The equation for Optimal Combination of Resources Condition is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Optimal Combination of Resources Condition:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Optimal Combination of Resources Condition?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MP</equation> in Marginal Revenue Product is: Marginal Product(MP).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MP</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{U}</equation> in Investment is: Unplanned investment.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>I_{U}</equation> in Investment?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>P</equation> in Present Value of Ordinary Annuities is: Present Value.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>P</equation> in Compound Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>P</equation> in Compound Interest?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL is: Price.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of call option c.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>c(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>r</equation> in Simple Interest is: Annual Rate.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>r</equation> in Simple Interest?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>P_{i}</equation> in Gini Coefficient is: The ratio of i-th group's population(P)/total population(P).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>P_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The Latex Code for equation Early Exercise for American Optionsis <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Early Exercise for American Options?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. Here is the brief introduction of Stock Prices as Geometric Brownian Motion:\n        Latex code for Stock Prices as Geometric Brownian Motion.\n        \n: Observed stock price S(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Stock Prices as Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Future Value of Ordinary Annuitiesis <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>", "tag": "Economics", "prompt": "What is the latex code of equation Future Value of Ordinary Annuities?"}
{"completion": " The equation for Banks Reserve Ratio is: <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>. Here is the brief introduction of Banks Reserve Ratio:\n        Latex code for the Banks Reserve Ratio.\n        \n \n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Cross-Price Elasticity of Demandis <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>t</equation> in Simple Interest is: Time (years).", "tag": "Economics", "prompt": "What is the meaning of <equation>t</equation> in Simple Interest?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Monte-Carlo Simulationsis <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Monte-Carlo Simulations?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion is: Stationary increments of Standard Brownian Motion.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\mu</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Annuities Due is: <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. Here is the brief introduction of Annuities Due:\n        Latex code for the Future Value of Annuities Due. I will briefly introduce the notations in this formulation. \n        The payment/deposit is at the BEGINNING of the period\n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you give me a brief introduction to Annuities Due?"}
{"completion": " The equation for Standard Brownian Motion is: <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. Here is the brief introduction of Standard Brownian Motion:\n        Latex code for the Standard Brownian Motion. I will briefly introduce the notations in this formulation. {Z(t)} has independent increments, and {Z(t)} has stationary increments such that Z (t + s) ? Z (t) follows standard normal distribution\n        \n: Value of Z at time stamp t\n: Stationary increments of Standard Brownian Motion\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Standard Brownian Motion?"}
{"completion": " The Latex Code for equation Profitis <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Profit?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Variable Cost is: Total Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>TC</equation> in Average Variable Cost?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Total Cost is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>TC</equation> in Average Total Cost?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>W_{i}</equation> in Gini Coefficient is: The ratio of i-th group's income/total income.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>W_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Standard Brownian Motionis <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Standard Brownian Motion?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>TC</equation> in Marginal Cost is: Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>TC</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Early Exercise for American Optionsis <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Early Exercise for American Options?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Elasticity of Supplyis <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Elasticity of Supply?"}
{"completion": " The Latex Code for equation Future Value of Ordinary Annuitiesis <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>", "tag": "Economics", "prompt": "How to write equation Future Value of Ordinary Annuities?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>i</equation> in Annuities Due is: Rate per period.", "tag": "Economics", "prompt": "What does the symbol mean <equation>i</equation> in Annuities Due?"}
{"completion": " The equation for Effective Rate is: <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. Here is the brief introduction of Effective Rate:\n        Latex code for the Effective Rate. I will briefly introduce the notations in this formulation. \n        \n: Effective Rate\n: Compute the effective rate if your loan/investment is compounded m times per year.\n: Compute the effective rate if your loan/investment is compounded continuously.\n\n\nRelated Documents\n\nInvestopedia Effective Rate\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "What's the meaning of Effective Rate?"}
{"completion": " The equation for Present Value of Ordinary Annuities is: <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. Here is the brief introduction of Present Value of Ordinary Annuities:\n        Latex code for the Present Value of Ordinary Annuities. I will briefly introduce the notations in this formulation.  \n        The payment is made at the END of the period. \n        \n: Present Value\n: Payment made in each period\n: Rate per period, usually i=r/m\n: Total number of times compounded, n=mt\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you explain Present Value of Ordinary Annuities?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand is: Percentage change in Price.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>% \\Delta P</equation> in Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Merchandise Trade Balanceis <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Merchandise Trade Balance?"}
{"completion": " The Latex Code for equation Average Productis <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Average Product?"}
{"completion": " The Latex Code for equation Optimal Consumption Ruleis <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Optimal Consumption Rule?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Total Costs is: Total Costs (TC).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{TC}</equation> in Total Costs?"}
{"completion": " The equation for Calls and Puts with Different Strikes is: <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. Here is the brief introduction of Calls and Puts with Different Strikes:\n\n        Latex code for the Calls and Puts with Different Strikes. For European calls and puts, with strike prices K_{1} and K_{2}, where K_{1} < K_{2}, we know the following.\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\n            American options, For three different options with strike prices K1 < K2 < K3:\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Calls and Puts with Different Strikes?"}
{"completion": " The equation for Asian Options is <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. The meaning of symbol <equation>G(T)</equation> in Asian Options is: Geometric average of option price at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>G(T)</equation> in Asian Options?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>P_{i}</equation> in Gini Coefficient is: The ratio of i-th group's population(P)/total population(P).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Marginal Revenue Product is: <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. Here is the brief introduction of Marginal Revenue Product:\n        Latex code for Marginal Revenue Product. The amount that an additional unit of a factor adds to a firm's total revenue during a period is called the marginal revenue product (MRP) of the factor. An additional unit of a factor of production adds to a firm\u2019s revenue in a two-step process: first, it increases the firm's output. Second, the increased output increases the firm\u2019s total revenue. We find marginal revenue product by multiplying the marginal product (MP) of the factor by the marginal revenue (MR). I will briefly introduce the notations in this formulation.  \n        \n: Marginal Product(MP)\n: Marginal Revenue(MR)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Marginal Revenue Product?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>X</equation> in Ito Lemma is: Diffusion.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>X</equation> in Ito Lemma?"}
{"completion": " The Latex Code for equation Total Costsis <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Total Costs?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>QI</equation> in Average Product is: Quantity of Input.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>QI</equation> in Average Product?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor is: Change in Labor(L).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor?"}
{"completion": " The equation for Optimal Consumption Rule is: <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. Here is the brief introduction of Optimal Consumption Rule:\n        Latex code for Optimal Consumption Rule. \n        \n: Marginal utility (MU)\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Optimal Consumption Rule?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A</equation> in Compound Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "What does the symbol mean <equation>A</equation> in Compound Interest?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Socially Optimal Level of Outputis <equation>\\\\text{MSB} = \\\\text{MSC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Socially Optimal Level of Output?"}
{"completion": " The Latex Code for equation Profitis <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Profit?"}
{"completion": " The Latex Code for equation Real Interest Rateis <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Real Interest Rate?"}
{"completion": " The equation for Gross Domestic Product Deflator is: <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Gross Domestic Product Deflator:\n        Latex code for Gross Domestic Product Deflator.\n        \n \n\nRelated Documents\n\nCorporate Finance Institute GDP Formula\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Gross Domestic Product Deflator?"}
{"completion": " The equation for Investment is: <equation>I=I_{P}+I_{U}</equation>. Here is the brief introduction of Investment:\n        Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).\n        \n: Investment\n: Planned investment\n: Unplanned investment\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Investment?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>MR</equation> in Price for a Competitive Firm is: Marginal revenue (MR).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MR</equation> in Price for a Competitive Firm?"}
{"completion": " The equation for Elasticity of Supply is: <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>. Here is the brief introduction of Elasticity of Supply:\n        Latex code for Elasticity of Supply. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Elasticity of Supply?"}
{"completion": " The equation for Elasticity of Supply is: <equation>\\\\text{Elasticity of Supply} = \\\\frac{\\\\text{Percentage Change in Quantity Supplied}}{\\\\text{Percentage Change in Price}}</equation>. Here is the brief introduction of Elasticity of Supply:\n        Latex code for Elasticity of Supply. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Elasticity of Supply?"}
{"completion": " The Latex Code for equation Gross Domestic Product Deflatoris <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Gross Domestic Product Deflator?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Total Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>Q</equation> in Average Total Cost?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts is: Risk-neutral equations.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>ATC</equation> in Average Total Cost is: Average Total Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>ATC</equation> in Average Total Cost?"}
{"completion": " The equation for Balanced Budget Multiplier is: <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. Here is the brief introduction of Balanced Budget Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Balanced Budget Multiplier?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MSB}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Equality of Leakages and Injections is: <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. Here is the brief introduction of Equality of Leakages and Injections:\n        Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy \u00e2\u20ac\u201c that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.\n        \n: Investment\n: Government Spending\n: Exports\n\n\nRelated Documents\n\nWhy are leakages equal to injections?\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Equality of Leakages and Injections?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>R</equation> in Future Value of Ordinary Annuities is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>R</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts is: Risk-neutral equations.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The Latex Code for equation Ito Lemmais <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Ito Lemma?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue is: Change in Total Revenue(TR).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{TR}</equation> in Marginal Revenue?"}
{"completion": " The equation for Black-Derman-Toy BDT is: <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. Here is the brief introduction of Black-Derman-Toy BDT:\n        Latex code for the Black-Derman-Toy BDT model. The BDT model is a commonly used interest rate model. The basic idea of the BDT model is to compute a binomial tree of short-term interest rates, with a flexible enough structure to match the data. Black, Derman, and Toy describe their tree as driven by the short-term rate, which they assume is lognormally distributed. Constructing the black-Derman-Toy tree, the first node is given by the prevailing 1-year rate R0.\n        The yield volatility for period-3 is .\n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nBlack-Derman-Toy Model Developed by Team at Goldman Sachs\nA Binomial Interest Rate Model and the Black-Derman-Toy Model\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Autonomous Spending Multiplieris <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Autonomous Spending Multiplier?"}
{"completion": " The Latex Code for equation Total Costsis <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Total Costs?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The related materials of Varying Times to Expiration is: 1.Investopedia Put Call Parity:<url>https://www.investopedia.com/terms/p/putcallparity.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Varying Times to Expiration?"}
{"completion": " The Latex Code for equation Total Costsis <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Total Costs?"}
{"completion": " The Latex Code for equation Asian Optionsis <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Asian Options?"}
{"completion": " The equation for Average Fixed Cost is: <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. Here is the brief introduction of Average Fixed Cost:\n        Latex code for the Allocative Average Fixed Cost. I will briefly introduce the notations in this formulation.  \n        \n: Total Fixed Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Average Fixed Cost?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{P}</equation> in Investment is: Planned investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>I_{P}</equation> in Investment?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is: <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. Here is the brief introduction of Geometric Brownian Motion SDEs:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Optimal Combination of Resources Condition is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Optimal Combination of Resources Condition:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Optimal Combination of Resources Condition?"}
{"completion": " The related materials of Consumption Function is: 1.Investopedia: Consumer Price Index:<url>https://www.investopedia.com/terms/c/consumerpriceindex.asp</url>;2.CPI Home : U.S. Bureau of Labor Statistics:<url>https://www.bls.gov/cpi/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Consumption Function?"}
{"completion": " The equation for Balanced Budget Multiplier is <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. The meaning of symbol <equation>MPC</equation> in Balanced Budget Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>MPC</equation> in Balanced Budget Multiplier?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost is: Change in Quantity.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Total Cost is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>TC</equation> in Average Total Cost?"}
{"completion": " The related materials of Average Product is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Average Product?"}
{"completion": " The related materials of Socially Optimal Level of Output is: 1.8-1-production-choices-and-costs-the-short-run:<url>https://open.lib.umn.edu/principleseconomics/chapter/8-1-production-choices-and-costs-the-short-run</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Socially Optimal Level of Output?"}
{"completion": " The Latex Code for equation Geometric Brownian Motion SDEsis <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma is: Stochastic differential equation for X(t).", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Present Value of Ordinary Annuities is: <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. Here is the brief introduction of Present Value of Ordinary Annuities:\n        Latex code for the Present Value of Ordinary Annuities. I will briefly introduce the notations in this formulation.  \n        The payment is made at the END of the period. \n        \n: Present Value\n: Payment made in each period\n: Rate per period, usually i=r/m\n: Total number of times compounded, n=mt\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you give me a brief introduction to Present Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Average Revenueis <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Average Revenue?"}
{"completion": " The Latex Code for equation Varying Times to Expirationis <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Varying Times to Expiration?"}
{"completion": " The equation for Allocative Efficiency Condition is: <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. Here is the brief introduction of Allocative Efficiency Condition:\n        Latex code for the Allocative Efficiency Condition. I will briefly introduce the notations in this formulation.  \n        Allocative efficiency occurs when consumer demand is completely met by supply. In other words, businesses are providing the exact supply that consumers want.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\nAllocative Efficiency: Definition, Example Productive Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Allocative Efficiency Condition?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Future Value of Ordinary Annuities is: <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. Here is the brief introduction of Future Value of Ordinary Annuities:\n        Latex code for the Future Value of Ordinary Annuities. The payment/deposit is at the END of the period. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "What's the meaning of Future Value of Ordinary Annuities?"}
{"completion": " The equation for Present Value of Ordinary Annuities is: <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. Here is the brief introduction of Present Value of Ordinary Annuities:\n        Latex code for the Present Value of Ordinary Annuities. I will briefly introduce the notations in this formulation.  \n        The payment is made at the END of the period. \n        \n: Present Value\n: Payment made in each period\n: Rate per period, usually i=r/m\n: Total number of times compounded, n=mt\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "I am interested in Present Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Call and Put Price Boundsis <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Call and Put Price Bounds?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Call Option Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Forwardsis <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Forwards?"}
{"completion": " The equation for Marginal Revenue is: <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Revenue:\n        Latex code for Marginal Revenue. \n        \n: Marginal Revenue\n: Change in Total Revenue(TR)\n: Change in Quantity(Q)\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Marginal Revenue?"}
{"completion": " The equation for Varying Times to Expiration is: <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. Here is the brief introduction of Varying Times to Expiration:\n\n            For American options, when expiration T2 > T1, the above equations holds.\n        \n\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Varying Times to Expiration?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Put Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Compound Interestis <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>", "tag": "Economics", "prompt": "How to write equation Compound Interest?"}
{"completion": " The Latex Code for equation Allocative Efficiency Conditionis <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Allocative Efficiency Condition?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{PQ}</equation> in Equation of Exchange is: Total spending on goods and services, measured as PY (or nominal GDP).", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>\\text{PQ}</equation> in Equation of Exchange?"}
{"completion": " The Latex Code for equation Black-Derman-Toy BDTis <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Black-Derman-Toy BDT?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSB</equation> in Allocative Efficiency Condition is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MSB</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSC</equation> in Allocative Efficiency Condition is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MSC</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MFC</equation> in Factor of Production Hiring Rule is: Marginal factor cost (MFC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MFC</equation> in Factor of Production Hiring Rule?"}
{"completion": " The Latex Code for equation Varying Times to Expirationis <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Varying Times to Expiration?"}
{"completion": " The equation for Compound Interest is: <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. Here is the brief introduction of Compound Interest:\n        Latex code for the Compound Interest. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Maturity Value\n: Principal/Present Value\n: Annual Rate (decimal)\n: Number of Compounding Periods per Year\n: Time (years)\n: Loan/investment is compounded continuously\n\n\nRelated Documents\n\nCompound Interest Calculator\nInvestopedia Compound Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "What's the meaning of Compound Interest?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs is: Volatility.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>F_{t,T}(S)</equation> in Forwards is: Forward Contract at strike price S.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>F_{t,T}(S)</equation> in Forwards?"}
{"completion": " The equation for Price Elasticity of Demand is: <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. Here is the brief introduction of Price Elasticity of Demand:\n        Latex code for Price Elasticity of Demand. Price Elasticity of Demand= Percentage change in quantity demanded / Percentage change in Price\n        \n: Percentage change in quantity demanded\n: Percentage change in Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Price Elasticity of Demand?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>TFC</equation> in Average Fixed Cost is: Total Fixed Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>TFC</equation> in Average Fixed Cost?"}
{"completion": " The equation for Consumer Price Index CPI is: <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Consumer Price Index CPI:\n        Latex code for Consumer Price Index CPI.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Consumer Price Index CPI?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio is: Sharpe ratio of any asset written on a GBM.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\phi = \\frac{a - r}{\\sigma}</equation> in Sharpe Ratio?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>i</equation> in Annuities Due is: Rate per period.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>i</equation> in Annuities Due?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MFC</equation> in Factor of Production Hiring Rule is: Marginal factor cost (MFC).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MFC</equation> in Factor of Production Hiring Rule?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Call Option Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Present Value of Ordinary Annuities is: <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. Here is the brief introduction of Present Value of Ordinary Annuities:\n        Latex code for the Present Value of Ordinary Annuities. I will briefly introduce the notations in this formulation.  \n        The payment is made at the END of the period. \n        \n: Present Value\n: Payment made in each period\n: Rate per period, usually i=r/m\n: Total number of times compounded, n=mt\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "What's the meaning of Present Value of Ordinary Annuities?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost is: Change in Quantity.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Ito Lemmais <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Ito Lemma?"}
{"completion": " The Latex Code for equation Varying Times to Expirationis <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Varying Times to Expiration?"}
{"completion": " The related materials of Average Total Cost is: ", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Average Total Cost?"}
{"completion": " The Latex Code for equation Production Efficiency Conditionis <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Production Efficiency Condition?"}
{"completion": " The equation for Price for a Competitive Firm is: <equation>P = MR</equation>. Here is the brief introduction of Price for a Competitive Firm:\n        Latex code for Price for a Competitive Firm.\n        \n: Marginal revenue (MR)\n: Price\n\n\nRelated Documents\n\nInvestopedia Price Elasticity of Demand\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Price for a Competitive Firm?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Equation of Exchange is <equation>\\\\text{MV} = \\\\text{PQ}</equation>. The meaning of symbol <equation>\\text{MV}</equation> in Equation of Exchange is: Total spending on goods and services, measured as Monetary Value.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>\\text{MV}</equation> in Equation of Exchange?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>R_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio is: Sharpe ratio.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC is: Change in the quantity of the factor.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue Product is: Marginal Revenue(MR).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MR</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Consumer Price Index CPI is: <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Consumer Price Index CPI:\n        Latex code for Consumer Price Index CPI.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Consumer Price Index CPI?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The Latex Code for equation Average Productis <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Average Product?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Optimal Combination of Resources Condition is: Price.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Marginal Cost is: <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Cost:\n        Latex code for Marginal Cost. \n        \n: Total Cost(TC)\n: Change in Total Cost(TC)\n: Quantity\n: Change in Quantity\n\n\nRelated Documents\n\nInvestopedia Marginal Cost\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Marginal Cost?"}
{"completion": " The equation for Total Costs is: <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. Here is the brief introduction of Total Costs:\n        Latex code for Socially Optimal Level of Output.\n        \n: Total Costs (TC)\n: Total Fixed Costs (TFC)\n: Total Variable Costs (TVC)\n\n\nRelated Documents\n\nTotal Variable Costs\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Total Costs?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{U}</equation> in Investment is: Unplanned investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>I_{U}</equation> in Investment?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>Q</equation> in Marginal Cost is: Quantity.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>Q</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Marginal Factor Cost MFCis <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Marginal Factor Cost MFC?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage is: Strike price of option 2.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Average Fixed Costis <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Average Fixed Cost?"}
{"completion": " The equation for Geometric Brownian Motion is: <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. Here is the brief introduction of Geometric Brownian Motion:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Geometric Brownian Motion?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>I</equation> in Simple Interest is: Interest Earned.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>I</equation> in Simple Interest?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage is: Strike price of option 2.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>K_{2}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The Latex Code for equation Early Exercise for American Optionsis <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Optimal Consumption Ruleis <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Optimal Consumption Rule?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is: <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. Here is the brief introduction of Geometric Brownian Motion SDEs:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity is: Price of put option p.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>p(S_{t}, K, t, T)</equation> in Put-Call Parity?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity is: .", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>Ke^{-r(T-t)}</equation> in Put-Call Parity?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded continuously..", "tag": "Economics", "prompt": "What does the symbol mean <equation>r_{e} = e^{r} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>P</equation> in Price for a Competitive Firm is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P</equation> in Price for a Competitive Firm?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A</equation> in Compound Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "What is the meaning of <equation>A</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Geometric Brownian Motionis <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Geometric Brownian Motion?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>MR</equation> in Price for a Competitive Firm is: Marginal revenue (MR).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MR</equation> in Price for a Competitive Firm?"}
{"completion": " The Latex Code for equation Marginal Revenue Productis <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Marginal Revenue Product?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>U</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{A}</equation> in Gini Coefficient is: Area between Line of Perfect Equality and Lorenz Curve..", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>S_{A}</equation> in Gini Coefficient?"}
{"completion": " The equation for Cross-Price Elasticity of Demand is: <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>. Here is the brief introduction of Cross-Price Elasticity of Demand:\n        Latex code for Cross-Price Elasticity of Demand. I will briefly introduce the notations in this formulation.  \n        \n\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Cross-Price Elasticity of Demand?"}
{"completion": " The related materials of Slope of the Total Product Curve is: 1.8-1-production-choices-and-costs-the-short-run:<url>https://open.lib.umn.edu/principleseconomics/chapter/8-1-production-choices-and-costs-the-short-run</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Slope of the Total Product Curve?"}
{"completion": " The Latex Code for equation Asian Optionsis <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Asian Options?"}
{"completion": " The equation for Gini Coefficient is: <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. Here is the brief introduction of Gini Coefficient:\n        Latex code for Gini Coefficient.  The Gini coefficient (Gini index or Gini ratio) is a statistical measure of economic inequality in a population. The coefficient measures the dispersion of income or distribution of wealth among the members of a population.\n        \n: Area between Line of Perfect Equality and Lorenz Curve.\n: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income).\n: The ratio of i-th group's income/total income\n: The ratio of cumulative i-th group's income(increasing order)/total income\n: The ratio of i-th group's population(P)/total population(P)\n\n\nRelated Documents\n\nCorporate Finance Institute Gini-coefficient\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Gini Coefficient?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue is: Change in Quantity(Q).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue?"}
{"completion": " The equation for Factor of Production Hiring Rule is: <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. Here is the brief introduction of Factor of Production Hiring Rule:\n        Latex code for Factor of Production Hiring Rule. I will briefly introduce the notations in this formulation.  \n        \n: Marginal revenue product\n: Marginal factor cost (MFC)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Factor of Production Hiring Rule?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{2}.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Gross Domestic Product Deflatoris <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Gross Domestic Product Deflator?"}
{"completion": " The Latex Code for equation Average Revenueis <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Average Revenue?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Marginal Revenue Product of Labor MRPLis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>U</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>Q_{i}</equation> in Gini Coefficient is: The ratio of cumulative i-th group's income(increasing order)/total income.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>Q_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue is: Change in Quantity(Q).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{Q}</equation> in Marginal Revenue?"}
{"completion": " The equation for Asian Options is: <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. Here is the brief introduction of Asian Options:\n        Latex code for the Asian options are options. Asian options are options that are based on averages in place of either the price or the strike. The average can be either an arithmetic average or a geometric average. Then to price the option replace either the strike or the price with the appropriate path-dependent average, calculate the payoffs, and then discount them.\n        \n: Arithmetic average of option price at time T\n: Geometric average of option price at time T\n\n\nRelated Documents\n\nWhat Is an Asian Option? How They Work Vs. Standard Options\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Asian Options?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. Here is the brief introduction of Risk-Neutral Valuation and Power Contracts:\n        Latex code for Risk-Neutral Valuation and Power Contracts.\n        \n: Payoff a power contract at time T\n: Price of the power contract\n: Risk-neutral equations\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Factor of Production Hiring Rule is: <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. Here is the brief introduction of Factor of Production Hiring Rule:\n        Latex code for Factor of Production Hiring Rule. I will briefly introduce the notations in this formulation.  \n        \n: Marginal revenue product\n: Marginal factor cost (MFC)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Factor of Production Hiring Rule?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>X</equation> in Ito Lemma is: Diffusion.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>X</equation> in Ito Lemma?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A</equation> in Compound Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>A</equation> in Compound Interest?"}
{"completion": " The equation for Unemployment Rate is: <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>. Here is the brief introduction of Unemployment Rate:\n        Latex code for Unemployment Rate.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Unemployment Rate?"}
{"completion": " The equation for Varying Times to Expiration is: <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. Here is the brief introduction of Varying Times to Expiration:\n\n            For American options, when expiration T2 > T1, the above equations holds.\n        \n\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Varying Times to Expiration?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC is: Change in total cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{TC}}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Allocative Efficiency Condition is: <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. Here is the brief introduction of Allocative Efficiency Condition:\n        Latex code for the Allocative Efficiency Condition. I will briefly introduce the notations in this formulation.  \n        Allocative efficiency occurs when consumer demand is completely met by supply. In other words, businesses are providing the exact supply that consumers want.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\nAllocative Efficiency: Definition, Example Productive Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Allocative Efficiency Condition?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>i</equation> in Future Value of Ordinary Annuities is: Rate per period.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>i</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Call Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Price Elasticity of Demandis <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Price Elasticity of Demand?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition is: Marginal Utility of F.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Profit is: <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. Here is the brief introduction of Profit:\n        Latex code for Price for a Competitive Firm.\n        \n: Total Revenue\n: Total Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Profit?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>g_{i}</equation> in Monte-Carlo Simulations is: The i-th simulated payoff.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>g_{i}</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Consumer Price Index CPIis <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Consumer Price Index CPI?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage is: Strike price of option 3.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>K_{3}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MRP</equation> in Factor of Production Hiring Rule is: Marginal revenue product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MRP</equation> in Factor of Production Hiring Rule?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>P</equation> in Price for a Competitive Firm is: Price.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P</equation> in Price for a Competitive Firm?"}
{"completion": " The Latex Code for equation Equality of Leakages and Injectionsis <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Equality of Leakages and Injections?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>P</equation> in Simple Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "What is the meaning of <equation>P</equation> in Simple Interest?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>n</equation> in Present Value of Ordinary Annuities is: Total number of times compounded, n=mt.", "tag": "Economics", "prompt": "What does the symbol mean <equation>n</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Bonds and Interest Rates is: <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. Here is the brief introduction of Bonds and Interest Rates:\n        Latex code for the Bonds and Interest Rates. The price of an s-year zero is P(0, S). The forward bond price formula  is calculated as . And the \n        non-continuous annualized rate is .\n        \n: Price of an s-year zero.\n: Forward Bond Price\n: Non-continuous annualized rate\n\n\nRelated Documents\n\nBond and Interest Rate\nUnderstanding Interest Rates, Inflation, and Bonds\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Consumer Price Index CPIis <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Consumer Price Index CPI?"}
{"completion": " The equation for Investment is: <equation>I=I_{P}+I_{U}</equation>. Here is the brief introduction of Investment:\n        Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).\n        \n: Investment\n: Planned investment\n: Unplanned investment\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Investment?"}
{"completion": " The equation for Socially Optimal Level of Output is: <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. Here is the brief introduction of Socially Optimal Level of Output:\n        Latex code for Socially Optimal Level of Output.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Socially Optimal Level of Output?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{U}</equation> in Investment is: Unplanned investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of <equation>I_{U}</equation> in Investment?"}
{"completion": " The equation for Future Value of Ordinary Annuities is: <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. Here is the brief introduction of Future Value of Ordinary Annuities:\n        Latex code for the Future Value of Ordinary Annuities. The payment/deposit is at the END of the period. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you explain Future Value of Ordinary Annuities?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma is: Stochastic differential equation for X(t).", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma?"}
{"completion": " The related materials of Compound Interest is: 1.Compound Interest Calculator:<url>https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator</url>;2.Investopedia Compound Interest:<url>https://www.investopedia.com/terms/c/compoundinterest.asp</url>;", "tag": "Economics", "prompt": "Can you help me find related materials of Compound Interest?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>U</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>t</equation> in Compound Interest is: Time (years).", "tag": "Economics", "prompt": "What is the meaning of <equation>t</equation> in Compound Interest?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{F}</equation> in Distributive Efficiency Condition is: Product of F.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The related materials of Profit is: 1.Profit:<url>https://www.investopedia.com/terms/p/profit.asp</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Profit?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>g_{i}</equation> in Monte-Carlo Simulations is: The i-th simulated payoff.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>g_{i}</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Nominal Interest Rateis <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Nominal Interest Rate?"}
{"completion": " The Latex Code for equation Price Elasticity of Demandis <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Varying Times to Expirationis <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Varying Times to Expiration?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>W_{i}</equation> in Gini Coefficient is: The ratio of i-th group's income/total income.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>W_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Put Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>MU</equation> in Optimal Consumption Rule is: Marginal utility (MU).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MU</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand is: Percentage change in quantity demanded.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\mu</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Stock Prices as Geometric Brownian Motionis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Marginal Revenue Product is: <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. Here is the brief introduction of Marginal Revenue Product:\n        Latex code for Marginal Revenue Product. The amount that an additional unit of a factor adds to a firm's total revenue during a period is called the marginal revenue product (MRP) of the factor. An additional unit of a factor of production adds to a firm\u2019s revenue in a two-step process: first, it increases the firm's output. Second, the increased output increases the firm\u2019s total revenue. We find marginal revenue product by multiplying the marginal product (MP) of the factor by the marginal revenue (MR). I will briefly introduce the notations in this formulation.  \n        \n: Marginal Product(MP)\n: Marginal Revenue(MR)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Marginal Revenue Product?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>Q</equation> in Marginal Cost is: Quantity.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>Q</equation> in Marginal Cost?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue is: Change in Total Revenue(TR).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue?"}
{"completion": " The Latex Code for equation Price for a Competitive Firmis <equation>P = MR</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Price for a Competitive Firm?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>S</equation> in Future Value of Ordinary Annuities is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>S</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Asian Optionsis <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Asian Options?"}
{"completion": " The equation for Real GDP is: <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>. Here is the brief introduction of Real GDP:\n        Latex code for Real GDP.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Real GDP?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>t</equation> in Simple Interest is: Time (years).", "tag": "Economics", "prompt": "What does the symbol mean <equation>t</equation> in Simple Interest?"}
{"completion": " The equation for Sharpe Ratio is: <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. Here is the brief introduction of Sharpe Ratio:\n        Latex code for Sharpe Ratio.\n        \n: Compounded Dividend Rate\n: Sharpe ratio\n: Sharpe ratio of any asset written on a GBM\n\n\nRelated Documents\n\nSharpe Ratio Formula and Definition With Examples\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Sharpe Ratio?"}
{"completion": " The Latex Code for equation Put-Call Parityis <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Put-Call Parity?"}
{"completion": " The equation for Call and Put Price Bounds is: <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. Here is the brief introduction of Call and Put Price Bounds:\n\n        Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.\n        \n\n: European Call Option Price\n: European Put Option Price\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Call and Put Price Bounds?"}
{"completion": " The equation for Average Variable Cost is: <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Variable Cost:\n        Latex code for the Average Variable Cost. I will briefly introduce the notations in this formulation.  \n        \n: Average Variable Cost\n: Total Variable Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Average Variable Cost?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>S</equation> in Annuities Due is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "What does the symbol mean <equation>S</equation> in Annuities Due?"}
{"completion": " The Latex Code for equation Equality of Leakages and Injectionsis <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Equality of Leakages and Injections?"}
{"completion": " The equation for Annuities Due is: <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. Here is the brief introduction of Annuities Due:\n        Latex code for the Future Value of Annuities Due. I will briefly introduce the notations in this formulation. \n        The payment/deposit is at the BEGINNING of the period\n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "Can you explain Annuities Due?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{1}.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>c(K_{1})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Bonds and Interest Ratesis <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Bonds and Interest Rates?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TR}</equation> in Profit is: Total Revenue.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{TR}</equation> in Profit?"}
{"completion": " The Latex Code for equation Socially Optimal Level of Outputis <equation>\\\\text{MSB} = \\\\text{MSC}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Socially Optimal Level of Output?"}
{"completion": " The equation for Varying Times to Expiration is <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>C(S_{t},K,t,T)</equation> in Varying Times to Expiration?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>AP</equation> in Average Product is: Average Product.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>AP</equation> in Average Product?"}
{"completion": " The Latex Code for equation Simple Interestis <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>", "tag": "Economics", "prompt": "Can you write equation Simple Interest?"}
{"completion": " The equation for Geometric Brownian Motion is: <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. Here is the brief introduction of Geometric Brownian Motion:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Geometric Brownian Motion?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\sigma</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>P_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Investment is: <equation>I=I_{P}+I_{U}</equation>. Here is the brief introduction of Investment:\n        Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).\n        \n: Investment\n: Planned investment\n: Unplanned investment\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Investment?"}
{"completion": " The equation for Marginal Cost is: <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Cost:\n        Latex code for Marginal Cost. \n        \n: Total Cost(TC)\n: Change in Total Cost(TC)\n: Quantity\n: Change in Quantity\n\n\nRelated Documents\n\nInvestopedia Marginal Cost\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Marginal Cost?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MRP</equation> in Factor of Production Hiring Rule is: Marginal revenue product.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MRP</equation> in Factor of Production Hiring Rule?"}
{"completion": " The equation for Marginal Product of Labor is: <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. Here is the brief introduction of Marginal Product of Labor:\n        Latex code for Marginal Product of Labor. \n        \n: Marginal Product of Labor\n: Change in Total Product(TP)\n: Change in Labor(L)\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Marginal Product of Labor?"}
{"completion": " The equation for Simple Interest is <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. The meaning of symbol <equation>P</equation> in Simple Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>P</equation> in Simple Interest?"}
{"completion": " The Latex Code for equation Call and Put Price Boundsis <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Call and Put Price Bounds?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition is: Marginal Utility of C.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MU_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Optimal Combination of Resources Conditionis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Optimal Combination of Resources Condition?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(t)</equation> in Monte-Carlo Simulations is: The stock price at time t, which is nearer to final stage stock price S(T).", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>S(t)</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Consumption Functionis <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Consumption Function?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>TP</equation> in Average Product is: Total Product.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>TP</equation> in Average Product?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>U</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>W_{i}</equation> in Gini Coefficient is: The ratio of i-th group's income/total income.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>W_{i}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Geometric Brownian Motionis <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Geometric Brownian Motion?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Profit is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{TC}</equation> in Profit?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t)</equation> in Standard Brownian Motion is: Value of Z at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Put-Call Parity is: <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. Here is the brief introduction of Put-Call Parity:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. Call options give the owner the right, but not the obligation, to buy an asset at some time in the future for a predetermined strike price. Put options give the owner the right to sell. The price of calls and puts is compared in the following put-call parity formula for European options.\n        \n: Price of call option c\n: Price of put option p\n: the present value of the strike price (x), \n: \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Put-Call Parity?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded m times per year..", "tag": "Economics", "prompt": "What does the symbol mean <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{F}</equation> in Distributive Efficiency Condition is: Product of F.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>P_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>n</equation> in Future Value of Ordinary Annuities is: Total number of times compounded.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>n</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Banks Reserve Ratiois <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Average Productis <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Average Product?"}
{"completion": " The equation for Profit-Maximizing Output Level is: <equation>MR = MC</equation>. Here is the brief introduction of Profit-Maximizing Output Level:\n        Latex code for Profit-Maximizing Output Level.\n        \n: Marginal Revenue\n: Marginal Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Profit-Maximizing Output Level?"}
{"completion": " The equation for Call and Put Price Bounds is: <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. Here is the brief introduction of Call and Put Price Bounds:\n\n        Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.\n        \n\n: European Call Option Price\n: European Put Option Price\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Call and Put Price Bounds?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion SDEs is: Volatility.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\sigma</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion SDEs is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>U</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Put Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P_{1}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>TFC</equation> in Average Fixed Cost is: Total Fixed Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>TFC</equation> in Average Fixed Cost?"}
{"completion": " The equation for Call and Put Price Bounds is: <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. Here is the brief introduction of Call and Put Price Bounds:\n\n        Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.\n        \n\n: European Call Option Price\n: European Put Option Price\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Call and Put Price Bounds?"}
{"completion": " The equation for Marginal Product of Labor is: <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. Here is the brief introduction of Marginal Product of Labor:\n        Latex code for Marginal Product of Labor. \n        \n: Marginal Product of Labor\n: Change in Total Product(TP)\n: Change in Labor(L)\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Marginal Product of Labor?"}
{"completion": " The equation for Average Revenue is: <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>. Here is the brief introduction of Average Revenue:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Average Revenue?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>n</equation> in Future Value of Ordinary Annuities is: Total number of times compounded.", "tag": "Economics", "prompt": "What does the symbol mean <equation>n</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Standard Brownian Motion is: <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. Here is the brief introduction of Standard Brownian Motion:\n        Latex code for the Standard Brownian Motion. I will briefly introduce the notations in this formulation. {Z(t)} has independent increments, and {Z(t)} has stationary increments such that Z (t + s) ? Z (t) follows standard normal distribution\n        \n: Value of Z at time stamp t\n: Stationary increments of Standard Brownian Motion\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Standard Brownian Motion?"}
{"completion": " The Latex Code for equation Cross-Price Elasticity of Demandis <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Monte-Carlo Simulations is: <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. Here is the brief introduction of Monte-Carlo Simulations:\n        Latex code for the Monte-Carlo Simulations of stock prices. I will briefly introduce the notations in this formulation. Monte-Carlo simulation simulates stock prices, calculate the payoff the option for each of those simulated prices, find the average payoff, and then discount the average payoff. Firstly, we start with iid uniform numbers u_{1} to u_{n}, calculate standard normal variable z_{i} as , convert to normal variable .  The variance of the Monte-Carlo estimate is calculated as . \n        \n: The stock price at time T\n: The stock price at time t, which is nearer to final stage stock price S(T)\n: The i-th simulated payoff\n: The variance of stock price\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Monte-Carlo Simulations?"}
{"completion": " The equation for Distributive Efficiency Condition is: <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. Here is the brief introduction of Distributive Efficiency Condition:\n        Latex code for Distributive Efficiency Condition. I will briefly introduce the notations in this formulation. Distributive efficiency is concerned with an equitable distribution of resources because of the law of diminishing marginal returns. The Law of diminishing marginal returns states that as consumption of a good increase we tend to get diminishing marginal utility. \n        \n: Marginal Utility of F\n: Product of F\n: Marginal Utility of C\n: Product of C\n\n\nRelated Documents\n\nDistributive Efficiency Definition\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Distributive Efficiency Condition?"}
{"completion": " The equation for Consumption Function is: <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>. Here is the brief introduction of Consumption Function:\n        Latex code for Consumption Function.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Consumption Function?"}
{"completion": " The equation for Calls and Puts Arbitrage is: <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. Here is the brief introduction of Calls and Puts Arbitrage:\n\n        Latex code for the Calls and Puts Arbitrage. Three different options have strike prices K1, K2, K3 and K1 < K2 < K3 holds.\n        An important formula for determining arbitrage opportunities comes from the following equations.\n        \n\n: Strike price of option 1\n: Strike price of option 2\n: Strike price of option 3\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Calls and Puts Arbitrage?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level is: Marginal Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The related materials of Autonomous Spending Multiplier is: 1.Principles Economics:<url>https://open.lib.umn.edu/principleseconomics/chapter/28-2-the-aggregate-expenditures-model/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Autonomous Spending Multiplier?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion is: Stationary increments of Standard Brownian Motion.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is: <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. Here is the brief introduction of Marginal Revenue Product of Labor MRPL:\n        Latex code for Marginal Revenue Product of Labor MRPL. The marginal revenue product of labor (MRPL) is the marginal product of labor (MPL) times the marginal revenue (which is the same as price under perfect competition) the firm obtains from additional units of output that result from hiring the additional unit of labor.\n        \n: Marginal Revenue Product of Labor\n: Marginal Product of Labor\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Marginal Revenue Product of Labor MRPL?"}
{"completion": " The Latex Code for equation Profit-Maximizing Output Levelis <equation>MR = MC</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Profit-Maximizing Output Level?"}
{"completion": " The Latex Code for equation Black-Derman-Toy BDTis <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Risk-Neutral Valuation and Power Contractsis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Black-Derman-Toy BDT is: <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. Here is the brief introduction of Black-Derman-Toy BDT:\n        Latex code for the Black-Derman-Toy BDT model. The BDT model is a commonly used interest rate model. The basic idea of the BDT model is to compute a binomial tree of short-term interest rates, with a flexible enough structure to match the data. Black, Derman, and Toy describe their tree as driven by the short-term rate, which they assume is lognormally distributed. Constructing the black-Derman-Toy tree, the first node is given by the prevailing 1-year rate R0.\n        The yield volatility for period-3 is .\n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nBlack-Derman-Toy Model Developed by Team at Goldman Sachs\nA Binomial Interest Rate Model and the Black-Derman-Toy Model\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Marginal Revenueis <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Marginal Revenue?"}
{"completion": " The Latex Code for equation Consumption Functionis <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Consumption Function?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue Product is: Marginal Revenue(MR).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MR</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Investment is: <equation>I=I_{P}+I_{U}</equation>. Here is the brief introduction of Investment:\n        Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).\n        \n: Investment\n: Planned investment\n: Unplanned investment\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Investment?"}
{"completion": " The equation for Average Total Cost is: <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Total Cost:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n: Average Total Cost\n: Total Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Average Total Cost?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is: <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. Here is the brief introduction of Cox-Ingersoll-Ross CIR:\n        Latex code for the Cox-Ingersoll-Ross model. \n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nCox-Ingersoll-Ross Model\nA THEORY OF THE TERM STRUCTURE OF INTEREST RATES\nCox-Ingersoll-Ross (CIR) model-Mathworks\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options is: put protection if the stock price should fall..", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>p(S_{t}, K)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TFC}</equation> in Total Costs is: Total Fixed Costs (TFC).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{TFC}</equation> in Total Costs?"}
{"completion": " The equation for Marginal Cost is: <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Cost:\n        Latex code for Marginal Cost. \n        \n: Total Cost(TC)\n: Change in Total Cost(TC)\n: Quantity\n: Change in Quantity\n\n\nRelated Documents\n\nInvestopedia Marginal Cost\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Marginal Cost?"}
{"completion": " The equation for Standard Brownian Motion is: <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. Here is the brief introduction of Standard Brownian Motion:\n        Latex code for the Standard Brownian Motion. I will briefly introduce the notations in this formulation. {Z(t)} has independent increments, and {Z(t)} has stationary increments such that Z (t + s) ? Z (t) follows standard normal distribution\n        \n: Value of Z at time stamp t\n: Stationary increments of Standard Brownian Motion\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Standard Brownian Motion?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>m</equation> in Compound Interest is: Number of Compounding Periods per Year.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>m</equation> in Compound Interest?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>P</equation> in Compound Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>P</equation> in Compound Interest?"}
{"completion": " The equation for Socially Optimal Level of Output is: <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. Here is the brief introduction of Socially Optimal Level of Output:\n        Latex code for Socially Optimal Level of Output.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\n8-1-production-choices-and-costs-the-short-run\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Socially Optimal Level of Output?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC is: Change in the quantity of the factor.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{f}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level is: Marginal Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MC}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>Q</equation> in Marginal Cost is: Quantity.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>Q</equation> in Marginal Cost?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor is: Change in Labor(L).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio is: Sharpe ratio.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio?"}
{"completion": " The related materials of Total Costs is: 1.Total Variable Costs:<url>https://corporatefinanceinstitute.com/resources/accounting/variable-costs/</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Total Costs?"}
{"completion": " The Latex Code for equation Equation of Exchangeis <equation>\\\\text{MV} = \\\\text{PQ}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Equation of Exchange?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue is: Change in Total Revenue(TR).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{TR}</equation> in Marginal Revenue?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded continuously..", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate?"}
{"completion": " The Latex Code for equation Cross-Price Elasticity of Demandis <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSC</equation> in Allocative Efficiency Condition is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MSC</equation> in Allocative Efficiency Condition?"}
{"completion": " The equation for Consumer Price Index CPI is: <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Consumer Price Index CPI:\n        Latex code for Consumer Price Index CPI.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Consumer Price Index CPI?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>R</equation> in Annuities Due is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>R</equation> in Annuities Due?"}
{"completion": " The Latex Code for equation Cox-Ingersoll-Ross CIRis <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. Here is the brief introduction of Stock Prices as Geometric Brownian Motion:\n        Latex code for Stock Prices as Geometric Brownian Motion.\n        \n: Observed stock price S(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(T)</equation> in Monte-Carlo Simulations is: The stock price at time T.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>S(T)</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Compound Interestis <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>", "tag": "Economics", "prompt": "What is the equation of Compound Interest?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t)</equation> in Standard Brownian Motion is: Value of Z at time stamp t.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\sigma</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>r</equation> in Forwards is: Interest Rate.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>r</equation> in Forwards?"}
{"completion": " The Latex Code for equation Balanced Budget Multiplieris <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Balanced Budget Multiplier?"}
{"completion": " The Latex Code for equation Effective Rateis <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>", "tag": "Economics", "prompt": "What is the equation of Effective Rate?"}
{"completion": " The equation for Real Interest Rate is: <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Real Interest Rate:\n        Latex code for Real Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Real Interest Rate?"}
{"completion": " The Latex Code for equation Marginal Revenue Productis <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Marginal Revenue Product?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>Q</equation> in Average Fixed Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>Q</equation> in Average Fixed Cost?"}
{"completion": " The Latex Code for equation Average Productis <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Average Product?"}
{"completion": " The Latex Code for equation Profitis <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Profit?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Marginal Revenue Product of Labor MRPL is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>X</equation> in Ito Lemma is: Diffusion.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>X</equation> in Ito Lemma?"}
{"completion": " The Latex Code for equation Cross-Price Elasticity of Demandis <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Unemployment Rate is: <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>. Here is the brief introduction of Unemployment Rate:\n        Latex code for Unemployment Rate.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Unemployment Rate?"}
{"completion": " The Latex Code for equation Cross-Price Elasticity of Demandis <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Price Elasticity of Demandis <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Price Elasticity of Demand?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition is: Marginal Utility of F.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MU_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Profit-Maximizing Output Levelis <equation>MR = MC</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Profit-Maximizing Output Level?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. Here is the brief introduction of Risk-Neutral Valuation and Power Contracts:\n        Latex code for Risk-Neutral Valuation and Power Contracts.\n        \n: Payoff a power contract at time T\n: Price of the power contract\n: Risk-neutral equations\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Average Revenue is: <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>. Here is the brief introduction of Average Revenue:\n        Latex code for the Average Revenue. I will briefly introduce the notations in this formulation.  \n        \n \n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Average Revenue?"}
{"completion": " The related materials of Put-Call Parity is: 1.Investopedia Put Call Parity:<url>https://www.investopedia.com/terms/p/putcallparity.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Put-Call Parity?"}
{"completion": " The Latex Code for equation Nominal Interest Rateis <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Nominal Interest Rate?"}
{"completion": " The related materials of Merchandise Trade Balance is: 1.Merchandise imports:<url>https://data.worldbank.org/indicator/TM.VAL.MRCH.CD.WT</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Merchandise Trade Balance?"}
{"completion": " The equation for Real Interest Rate is: <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Real Interest Rate:\n        Latex code for Real Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Real Interest Rate?"}
{"completion": " The Latex Code for equation Cox-Ingersoll-Ross CIRis <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts is: Price of the power contract.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>r</equation> in Compound Interest is: Annual Rate (decimal).", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>r</equation> in Compound Interest?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates is: Forward Bond Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>m</equation> in Compound Interest is: Number of Compounding Periods per Year.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>m</equation> in Compound Interest?"}
{"completion": " The equation for Gini Coefficient is: <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. Here is the brief introduction of Gini Coefficient:\n        Latex code for Gini Coefficient.  The Gini coefficient (Gini index or Gini ratio) is a statistical measure of economic inequality in a population. The coefficient measures the dispersion of income or distribution of wealth among the members of a population.\n        \n: Area between Line of Perfect Equality and Lorenz Curve.\n: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income).\n: The ratio of i-th group's income/total income\n: The ratio of cumulative i-th group's income(increasing order)/total income\n: The ratio of i-th group's population(P)/total population(P)\n\n\nRelated Documents\n\nCorporate Finance Institute Gini-coefficient\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Gini Coefficient?"}
{"completion": " The Latex Code for equation Monte-Carlo Simulationsis <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Monte-Carlo Simulations?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Total Cost is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>TC</equation> in Average Total Cost?"}
{"completion": " The equation for Marginal Revenue is: <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. Here is the brief introduction of Marginal Revenue:\n        Latex code for Marginal Revenue. \n        \n: Marginal Revenue\n: Change in Total Revenue(TR)\n: Change in Quantity(Q)\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Marginal Revenue?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue is: Change in Quantity(Q).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Revenue?"}
{"completion": " The Latex Code for equation Marginal Costis <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Marginal Cost?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Profit-Maximizing Output Level is: <equation>MR = MC</equation>. Here is the brief introduction of Profit-Maximizing Output Level:\n        Latex code for Profit-Maximizing Output Level.\n        \n: Marginal Revenue\n: Marginal Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Profit-Maximizing Output Level?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{U}</equation> in Investment is: Unplanned investment.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>I_{U}</equation> in Investment?"}
{"completion": " The Latex Code for equation Profitis <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Profit?"}
{"completion": " The equation for Nominal Interest Rate is: <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Nominal Interest Rate:\n        Latex code for Nominal Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Nominal Interest Rate?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion SDEs is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>U</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Put-Call Parityis <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Put-Call Parity?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>S</equation> in Future Value of Ordinary Annuities is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "What is the meaning of <equation>S</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Average Variable Costis <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Average Variable Cost?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>U</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Early Exercise for American Options is: <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. Here is the brief introduction of Early Exercise for American Options:\n\n            So we exercise the call option if the pros are greater than the cons, specifically, we exercise if:\n        \n\n: The cons are that we have to pay the strike earlier and therefore miss the interest on that money and we lose the put protection if the stock price should fall. So we exercise the call option if the pros are greater than the cons. \n: Early Exercise getting the stock's dividend payments\n: Pay the strike earlier and therefore miss the interest on that money\n: put protection if the stock price should fall.\n: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise. \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Early Exercise for American Options?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>n</equation> in Future Value of Ordinary Annuities is: Total number of times compounded.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>n</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Real GDP is: <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>. Here is the brief introduction of Real GDP:\n        Latex code for Real GDP.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Real GDP?"}
{"completion": " The Latex Code for equation Average Fixed Costis <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Average Fixed Cost?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MR</equation> in Marginal Revenue?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. Here is the brief introduction of Stock Prices as Geometric Brownian Motion:\n        Latex code for Stock Prices as Geometric Brownian Motion.\n        \n: Observed stock price S(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Stock Prices as Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Marginal Factor Cost MFCis <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Marginal Factor Cost MFC?"}
{"completion": " The related materials of Real GDP is: 1.Merchandise imports:<url>https://data.worldbank.org/indicator/TM.VAL.MRCH.CD.WT</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Real GDP?"}
{"completion": " The equation for Average Variable Cost is: <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. Here is the brief introduction of Average Variable Cost:\n        Latex code for the Average Variable Cost. I will briefly introduce the notations in this formulation.  \n        \n: Average Variable Cost\n: Total Variable Cost\n: Quantity of Output\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Average Variable Cost?"}
{"completion": " The Latex Code for equation Average Revenueis <equation>\\\\text{Average Revenue} = \\\\frac{\\\\text{Total Revenue}}{\\\\text{Quantity}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Average Revenue?"}
{"completion": " The Latex Code for equation Price for a Competitive Firmis <equation>P = MR</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Price for a Competitive Firm?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>MPL</equation> in Marginal Product of Labor is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MPL</equation> in Marginal Product of Labor?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage is: Strike price of option 3.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>Y(t)</equation> in Geometric Brownian Motion?"}
{"completion": " The related materials of Balanced Budget Multiplier is: 1.Principles Economics:<url>https://open.lib.umn.edu/principleseconomics/chapter/28-2-the-aggregate-expenditures-model/</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Balanced Budget Multiplier?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A = Pe^{rt}</equation> in Compound Interest is: Loan/investment is compounded continuously.", "tag": "Economics", "prompt": "What does the symbol mean <equation>A = Pe^{rt}</equation> in Compound Interest?"}
{"completion": " The equation for Average Product is: <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. Here is the brief introduction of Average Product:\n        Latex code for the Average Product. I will briefly introduce the notations in this formulation.  \n        \n: Average Product\n: Total Product\n: Quantity of Input\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Average Product?"}
{"completion": " The Latex Code for equation Calls and Puts with Different Strikesis <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Cox-Ingersoll-Ross CIRis <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Cox-Ingersoll-Ross CIR?"}
{"completion": " The Latex Code for equation Bonds and Interest Ratesis <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Bonds and Interest Rates?"}
{"completion": " The equation for Marginal Factor Cost MFC is: <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. Here is the brief introduction of Marginal Factor Cost MFC:\n        Latex code for Marginal Revenue Product of Labor MRPL. Marginal factor cost (MFC) is the change in total cost (\\Delta \\text{TC}}) divided by the change in the quantity of the factor:\n        \n: Marginal Factor Cost\n: Change in total cost\n: Change in the quantity of the factor\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Marginal Factor Cost MFC?"}
{"completion": " The equation for Future Value of Ordinary Annuities is: <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. Here is the brief introduction of Future Value of Ordinary Annuities:\n        Latex code for the Future Value of Ordinary Annuities. The payment/deposit is at the END of the period. I will briefly introduce the notations in this formulation. \n        \n: Future Value/Total amount accrued\n: Payment/Deposit made in each period\n: Rate per period\n: Total number of times compounded\n\n\nRelated Documents\n\nOrdinary Annuity\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "I am interested in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>n</equation> in Present Value of Ordinary Annuities is: Total number of times compounded, n=mt.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>n</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Sharpe Ratio is: <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. Here is the brief introduction of Sharpe Ratio:\n        Latex code for Sharpe Ratio.\n        \n: Compounded Dividend Rate\n: Sharpe ratio\n: Sharpe ratio of any asset written on a GBM\n\n\nRelated Documents\n\nSharpe Ratio Formula and Definition With Examples\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Sharpe Ratio?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I</equation> in Investment is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>I</equation> in Investment?"}
{"completion": " The equation for Total Costs is: <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. Here is the brief introduction of Total Costs:\n        Latex code for Socially Optimal Level of Output.\n        \n: Total Costs (TC)\n: Total Fixed Costs (TFC)\n: Total Variable Costs (TVC)\n\n\nRelated Documents\n\nTotal Variable Costs\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Total Costs?"}
{"completion": " The Latex Code for equation Distributive Efficiency Conditionis <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Distributive Efficiency Condition?"}
{"completion": " The equation for Put-Call Parity is <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. The meaning of symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity is: the present value of the strike price (x),.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>F^{P}_{t,T}(S)</equation> in Put-Call Parity?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{A}</equation> in Gini Coefficient is: Area between Line of Perfect Equality and Lorenz Curve..", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>S_{A}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Stock Prices as Geometric Brownian Motionis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>R</equation> in Annuities Due is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>R</equation> in Annuities Due?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MRP</equation> in Factor of Production Hiring Rule is: Marginal revenue product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MRP</equation> in Factor of Production Hiring Rule?"}
{"completion": " The Latex Code for equation Call and Put Price Boundsis <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Call and Put Price Bounds?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Total Cost is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>TC</equation> in Average Total Cost?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{2}.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The equation for Autonomous Spending Multiplier is <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. The meaning of symbol <equation>MPC</equation> in Autonomous Spending Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>MPC</equation> in Autonomous Spending Multiplier?"}
{"completion": " The Latex Code for equation Simple Interestis <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>", "tag": "Economics", "prompt": "What is the latex code of equation Simple Interest?"}
{"completion": " The equation for Factor of Production Hiring Rule is <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. The meaning of symbol <equation>MFC</equation> in Factor of Production Hiring Rule is: Marginal factor cost (MFC).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MFC</equation> in Factor of Production Hiring Rule?"}
{"completion": " The related materials of Present Value of Ordinary Annuities is: 1.Ordinary Annuity:<url>https://www.investopedia.com/terms/o/ordinaryannuity.asp</url>;", "tag": "Economics", "prompt": "Can you help me find related materials of Present Value of Ordinary Annuities?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost is: Change in Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost?"}
{"completion": " The equation for Allocative Efficiency Condition is <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. The meaning of symbol <equation>MSC</equation> in Allocative Efficiency Condition is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MSC</equation> in Allocative Efficiency Condition?"}
{"completion": " The Latex Code for equation Present Value of Ordinary Annuitiesis <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>", "tag": "Economics", "prompt": "How to write equation Present Value of Ordinary Annuities?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TR}</equation> in Profit is: Total Revenue.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{TR}</equation> in Profit?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost is: Change in Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations is: The variance of stock price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>e^{-2rT} \\times \\frac{s^{2}}{n}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve is: Total Product Curve.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{TPC}</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates is: Forward Bond Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Calls and Puts with Different Strikesis <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Calls and Puts with Different Strikes?"}
{"completion": " The equation for Geometric Brownian Motion is: <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. Here is the brief introduction of Geometric Brownian Motion:\n        Latex code for the Geometric Brownian Motion. \n        \n: Observed value Y(t) at time stamp t\n: Any normal random variable\n: Drift coefficient\n: Volatility\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Geometric Brownian Motion?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition is: Marginal Utility of F.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Put-Call Parity is: <equation>c(S_{t}, K, t, T) - p(S_{t}, K, t, T) = F^{P}_{t,T}(S) - Ke^{-r(T-t)}</equation>. Here is the brief introduction of Put-Call Parity:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. Call options give the owner the right, but not the obligation, to buy an asset at some time in the future for a predetermined strike price. Put options give the owner the right to sell. The price of calls and puts is compared in the following put-call parity formula for European options.\n        \n: Price of call option c\n: Price of put option p\n: the present value of the strike price (x), \n: \n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Put-Call Parity?"}
{"completion": " The related materials of Call and Put Price Bounds is: 1.Investopedia Put Call Parity:<url>https://www.investopedia.com/terms/p/putcallparity.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Call and Put Price Bounds?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options is: Pay the strike earlier and therefore miss the interest on that money.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>K(1 ? e^{?r(T ?t)})</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>i</equation> in Present Value of Ordinary Annuities is: Rate per period, usually i=r/m.", "tag": "Economics", "prompt": "What is the meaning of <equation>i</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Varying Times to Expiration is: <equation>T_{2} \\\\ge T_{1} \\\\\\\\\\ C(S_{t},K,t,T_{2}) \\\\ge C(S_{t},K,t,T_{1}) \\\\le S_{t} \\\\\\\\\\ P(S_{t},K,t,T_{2}) \\\\ge P(S_{t},K,t,T_{1}) \\\\le S_{t}</equation>. Here is the brief introduction of Varying Times to Expiration:\n\n            For American options, when expiration T2 > T1, the above equations holds.\n        \n\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Varying Times to Expiration?"}
{"completion": " The equation for Merchandise Trade Balance is: <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>. Here is the brief introduction of Merchandise Trade Balance:\n        Latex code for Merchandise Trade Balance.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Merchandise Trade Balance?"}
{"completion": " The equation for Black-Derman-Toy BDT is: <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. Here is the brief introduction of Black-Derman-Toy BDT:\n        Latex code for the Black-Derman-Toy BDT model. The BDT model is a commonly used interest rate model. The basic idea of the BDT model is to compute a binomial tree of short-term interest rates, with a flexible enough structure to match the data. Black, Derman, and Toy describe their tree as driven by the short-term rate, which they assume is lognormally distributed. Constructing the black-Derman-Toy tree, the first node is given by the prevailing 1-year rate R0.\n        The yield volatility for period-3 is .\n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nBlack-Derman-Toy Model Developed by Team at Goldman Sachs\nA Binomial Interest Rate Model and the Black-Derman-Toy Model\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Black-Derman-Toy BDT?"}
{"completion": " The equation for Real GDP is: <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>. Here is the brief introduction of Real GDP:\n        Latex code for Real GDP.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Real GDP?"}
{"completion": " The equation for Cross-Price Elasticity of Demand is: <equation>\\\\text{Elasticity of Demand} = \\\\frac{\\\\text{Percentage Change in Quantity Demanded of Good X}}{\\\\text{Percentage Change in Price of Good Y}}</equation>. Here is the brief introduction of Cross-Price Elasticity of Demand:\n        Latex code for Cross-Price Elasticity of Demand. I will briefly introduce the notations in this formulation.  \n        \n\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Cross-Price Elasticity of Demand?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve is: Total Product Curve.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand is: Percentage change in Price.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>% \\Delta P</equation> in Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Total Costsis <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Total Costs?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>S</equation> in Annuities Due is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "What is the meaning of <equation>S</equation> in Annuities Due?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MC}</equation> in Profit-Maximizing Output Level is: Marginal Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MC}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>FV</equation> in Forwards is: Future Value.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>FV</equation> in Forwards?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(0, S)</equation> in Bonds and Interest Rates is: Price of an s-year zero..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P(0, S)</equation> in Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Gross Domestic Product Deflatoris <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Gross Domestic Product Deflator?"}
{"completion": " The Latex Code for equation Marginal Revenueis <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Marginal Revenue?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates is: Forward Bond Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>F_{t,T}[P(T, T+s)]</equation> in Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Marginal Revenue Product of Labor MRPLis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Nominal Interest Rate is: <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Nominal Interest Rate:\n        Latex code for Nominal Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Nominal Interest Rate?"}
{"completion": " The equation for Unemployment Rate is: <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>. Here is the brief introduction of Unemployment Rate:\n        Latex code for Unemployment Rate.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Unemployment Rate?"}
{"completion": " The equation for Black-Derman-Toy BDT is: <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. Here is the brief introduction of Black-Derman-Toy BDT:\n        Latex code for the Black-Derman-Toy BDT model. The BDT model is a commonly used interest rate model. The basic idea of the BDT model is to compute a binomial tree of short-term interest rates, with a flexible enough structure to match the data. Black, Derman, and Toy describe their tree as driven by the short-term rate, which they assume is lognormally distributed. Constructing the black-Derman-Toy tree, the first node is given by the prevailing 1-year rate R0.\n        The yield volatility for period-3 is .\n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nBlack-Derman-Toy Model Developed by Team at Goldman Sachs\nA Binomial Interest Rate Model and the Black-Derman-Toy Model\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you explain Black-Derman-Toy BDT?"}
{"completion": " The related materials of Bonds and Interest Rates is: 1.Understanding Interest Rates, Inflation, and Bonds:<url>https://www.investopedia.com/articles/bonds/09/bond-market-interest-rates.asp</url>;2.Bond and Interest Rate:<url>https://www.wsj.com/market-data/bonds</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Real GDPis <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Real GDP?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{TC}</equation> in Marginal Cost is: Change in Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{TC}</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Consumer Price Index CPIis <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the latex code of equation Consumer Price Index CPI?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>TC</equation> in Marginal Cost is: Total Cost(TC).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>TC</equation> in Marginal Cost?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{C}</equation> in Distributive Efficiency Condition is: Product of C.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Standard Brownian Motionis <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>", "tag": "Financial,Economics", "prompt": "What is the equation of Standard Brownian Motion?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts is: Risk-neutral equations.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)]</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{X}</equation> in Equality of Leakages and Injections is: Exports.", "tag": "Economics,MacroEconomics", "prompt": "What does the symbol mean <equation>\\text{X}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio is: Sharpe ratio.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>\\phi = \\frac{m + \\delta -r }{s}</equation> in Sharpe Ratio?"}
{"completion": " The equation for Marginal Factor Cost MFC is: <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. Here is the brief introduction of Marginal Factor Cost MFC:\n        Latex code for Marginal Revenue Product of Labor MRPL. Marginal factor cost (MFC) is the change in total cost (\\Delta \\text{TC}}) divided by the change in the quantity of the factor:\n        \n: Marginal Factor Cost\n: Change in total cost\n: Change in the quantity of the factor\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Marginal Factor Cost MFC?"}
{"completion": " The equation for Call and Put Price Bounds is: <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. Here is the brief introduction of Call and Put Price Bounds:\n\n        Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.\n        \n\n: European Call Option Price\n: European Put Option Price\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Call and Put Price Bounds?"}
{"completion": " The equation for Banks Reserve Ratio is: <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>. Here is the brief introduction of Banks Reserve Ratio:\n        Latex code for the Banks Reserve Ratio.\n        \n \n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Banks Reserve Ratio?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage is: Strike price of option 1.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>K_{1}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: For puts options, the pros are the interest earned on the strike. The cons are the lost dividends on owning the stock and the call protection should the stock price rise..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Total Costs is: <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. Here is the brief introduction of Total Costs:\n        Latex code for Socially Optimal Level of Output.\n        \n: Total Costs (TC)\n: Total Fixed Costs (TFC)\n: Total Variable Costs (TVC)\n\n\nRelated Documents\n\nTotal Variable Costs\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Total Costs?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is: <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. Here is the brief introduction of Cox-Ingersoll-Ross CIR:\n        Latex code for the Cox-Ingersoll-Ross model. \n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nCox-Ingersoll-Ross Model\nA THEORY OF THE TERM STRUCTURE OF INTEREST RATES\nCox-Ingersoll-Ross (CIR) model-Mathworks\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Cox-Ingersoll-Ross CIR?"}
{"completion": " The related materials of Stock Prices as Geometric Brownian Motion is: 1.Geometric Brownian Motion:<url>https://www.quantstart.com/articles/Geometric-Brownian-Motion/</url>;2.Geometric Brownian motion:<url>http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GBM.pdf</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Profit is: <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. Here is the brief introduction of Profit:\n        Latex code for Price for a Competitive Firm.\n        \n: Total Revenue\n: Total Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Profit?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{1}</equation> in Calls and Puts Arbitrage is: Strike price of option 1.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>K_{1}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>MU</equation> in Optimal Consumption Rule is: Marginal utility (MU).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MU</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded continuously..", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>r_{e} = e^{r} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>R</equation> in Future Value of Ordinary Annuities is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "What does the symbol mean <equation>R</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Average Variable Costis <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Average Variable Cost?"}
{"completion": " The equation for Banks Reserve Ratio is: <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>. Here is the brief introduction of Banks Reserve Ratio:\n        Latex code for the Banks Reserve Ratio.\n        \n \n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Early Exercise for American Optionsis <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Early Exercise for American Options?"}
{"completion": " The equation for Distributive Efficiency Condition is: <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. Here is the brief introduction of Distributive Efficiency Condition:\n        Latex code for Distributive Efficiency Condition. I will briefly introduce the notations in this formulation. Distributive efficiency is concerned with an equitable distribution of resources because of the law of diminishing marginal returns. The Law of diminishing marginal returns states that as consumption of a good increase we tend to get diminishing marginal utility. \n        \n: Marginal Utility of F\n: Product of F\n: Marginal Utility of C\n: Product of C\n\n\nRelated Documents\n\nDistributive Efficiency Definition\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Distributive Efficiency Condition?"}
{"completion": " The equation for Balanced Budget Multiplier is: <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. Here is the brief introduction of Balanced Budget Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Balanced Budget Multiplier?"}
{"completion": " The Latex Code for equation Gross Domestic Product Deflatoris <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Gross Domestic Product Deflator?"}
{"completion": " The Latex Code for equation Bonds and Interest Ratesis <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Consumer Price Index CPIis <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Consumer Price Index CPI?"}
{"completion": " The Latex Code for equation Merchandise Trade Balanceis <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Merchandise Trade Balance?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Put Option Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>p(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The Latex Code for equation Consumer Price Index CPIis <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Consumer Price Index CPI?"}
{"completion": " The Latex Code for equation Gini Coefficientis <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Gini Coefficient?"}
{"completion": " The Latex Code for equation Call and Put Price Boundsis <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Call and Put Price Bounds?"}
{"completion": " The equation for Allocative Efficiency Condition is: <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>. Here is the brief introduction of Allocative Efficiency Condition:\n        Latex code for the Allocative Efficiency Condition. I will briefly introduce the notations in this formulation.  \n        Allocative efficiency occurs when consumer demand is completely met by supply. In other words, businesses are providing the exact supply that consumers want.\n        \n: Marginal Social Benefit\n: Marginal Social Cost\n\n\nRelated Documents\n\nAllocative Efficiency: Definition, Example Productive Efficiency\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Allocative Efficiency Condition?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(t)</equation> in Monte-Carlo Simulations is: The stock price at time t, which is nearer to final stage stock price S(T).", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>S(t)</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Marginal Factor Cost MFC is: <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. Here is the brief introduction of Marginal Factor Cost MFC:\n        Latex code for Marginal Revenue Product of Labor MRPL. Marginal factor cost (MFC) is the change in total cost (\\Delta \\text{TC}}) divided by the change in the quantity of the factor:\n        \n: Marginal Factor Cost\n: Change in total cost\n: Change in the quantity of the factor\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Please give me detailed tutorial of Marginal Factor Cost MFC?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{2}</equation> in Calls and Puts Arbitrage is: Strike price of option 2.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>K_{2}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Equality of Leakages and Injections is <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. The meaning of symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "Can you explain the symbol <equation>\\text{I}</equation> in Equality of Leakages and Injections?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Price Elasticity of Demand is <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>. The meaning of symbol <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand is: Percentage change in quantity demanded.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>% \\Delta Q_{d}</equation> in Price Elasticity of Demand?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>P</equation> in Present Value of Ordinary Annuities is: Present Value.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>P</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. The meaning of symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts is: Price of the power contract.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>F^{p}_{t, T}(S^{a})</equation> in Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The Latex Code for equation Merchandise Trade Balanceis <equation>\\\\text{Merchandise Trade Balance}=\\\\text{Value of Merchandise Exports} - \\\\text{Value of Merchandise Imports}</equation>", "tag": "Economics,MacroEconomics", "prompt": "How to write equation Merchandise Trade Balance?"}
{"completion": " The equation for Average Fixed Cost is <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>. The meaning of symbol <equation>Q</equation> in Average Fixed Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>Q</equation> in Average Fixed Cost?"}
{"completion": " The equation for Risk-Neutral Valuation and Power Contracts is: <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>. Here is the brief introduction of Risk-Neutral Valuation and Power Contracts:\n        Latex code for Risk-Neutral Valuation and Power Contracts.\n        \n: Payoff a power contract at time T\n: Price of the power contract\n: Risk-neutral equations\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Please give me detailed tutorial of Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MR}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options is: put protection if the stock price should fall..", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>S</equation> in Annuities Due is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>S</equation> in Annuities Due?"}
{"completion": " The related materials of Forwards is: 1.Investopedia Simple Interest:<url>https://www.investopedia.com/terms/s/simple_interest.asp</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Forwards?"}
{"completion": " The Latex Code for equation Geometric Brownian Motion SDEsis <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Average Total Costis <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Average Total Cost?"}
{"completion": " The equation for Marginal Product of Labor is: <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. Here is the brief introduction of Marginal Product of Labor:\n        Latex code for Marginal Product of Labor. \n        \n: Marginal Product of Labor\n: Change in Total Product(TP)\n: Change in Labor(L)\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Investmentis <equation>I=I_{P}+I_{U}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Investment?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT is: 1-year interest rate..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>R_{0}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Gini Coefficientis <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Gini Coefficient?"}
{"completion": " The equation for Simple Interest is: <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. Here is the brief introduction of Simple Interest:\n        Latex code for the Simple Interest. I will briefly introduce the notations in this formulation. \n        \n: Interest Earned\n: Principal/Present Value\n: Annual Rate\n: Time (years)\n: Future Value/Maturity Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "What's the meaning of Simple Interest?"}
{"completion": " The Latex Code for equation Geometric Brownian Motion SDEsis <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>t</equation> in Compound Interest is: Time (years).", "tag": "Economics", "prompt": "Can you explain the symbol <equation>t</equation> in Compound Interest?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>i</equation> in Present Value of Ordinary Annuities is: Rate per period, usually i=r/m.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>i</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Gross Domestic Product Deflator is: <equation>\\\\text{GDP Deflator}= \\\\frac{\\\\text{Current Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Current Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Gross Domestic Product Deflator:\n        Latex code for Gross Domestic Product Deflator.\n        \n \n\nRelated Documents\n\nCorporate Finance Institute GDP Formula\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Gross Domestic Product Deflator?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>n</equation> in Annuities Due is: Total number of times compounded.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>n</equation> in Annuities Due?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve is: Total Product Curve.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{TPC}</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{C}</equation> in Distributive Efficiency Condition is: Product of C.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>t</equation> in Compound Interest is: Time (years).", "tag": "Economics", "prompt": "What does the symbol mean <equation>t</equation> in Compound Interest?"}
{"completion": " The equation for Total Costs is: <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. Here is the brief introduction of Total Costs:\n        Latex code for Socially Optimal Level of Output.\n        \n: Total Costs (TC)\n: Total Fixed Costs (TFC)\n: Total Variable Costs (TVC)\n\n\nRelated Documents\n\nTotal Variable Costs\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "I am interested in Total Costs?"}
{"completion": " The Latex Code for equation Present Value of Ordinary Annuitiesis <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>", "tag": "Economics", "prompt": "Show me the latex code of equation Present Value of Ordinary Annuities?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion is: Observed stock price S(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>S(t)</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P_{1}</equation> in Black-Derman-Toy BDT is: Observed year-1 price of a 1-year bond.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>P_{1}</equation> in Black-Derman-Toy BDT?"}
{"completion": " The equation for Real Interest Rate is: <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Real Interest Rate:\n        Latex code for Real Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Real Interest Rate?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>P</equation> in Optimal Consumption Rule is: Price.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\text{MRP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>MU</equation> in Optimal Consumption Rule is: Marginal utility (MU).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MU</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output is: Marginal Social Benefit.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MSB}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>\\mu</equation> in Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\mu</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Marginal Revenue Product is: <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. Here is the brief introduction of Marginal Revenue Product:\n        Latex code for Marginal Revenue Product. The amount that an additional unit of a factor adds to a firm's total revenue during a period is called the marginal revenue product (MRP) of the factor. An additional unit of a factor of production adds to a firm\u2019s revenue in a two-step process: first, it increases the firm's output. Second, the increased output increases the firm\u2019s total revenue. We find marginal revenue product by multiplying the marginal product (MP) of the factor by the marginal revenue (MR). I will briefly introduce the notations in this formulation.  \n        \n: Marginal Product(MP)\n: Marginal Revenue(MR)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Marginal Revenue Product?"}
{"completion": " The equation for Black-Derman-Toy BDT is: <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. Here is the brief introduction of Black-Derman-Toy BDT:\n        Latex code for the Black-Derman-Toy BDT model. The BDT model is a commonly used interest rate model. The basic idea of the BDT model is to compute a binomial tree of short-term interest rates, with a flexible enough structure to match the data. Black, Derman, and Toy describe their tree as driven by the short-term rate, which they assume is lognormally distributed. Constructing the black-Derman-Toy tree, the first node is given by the prevailing 1-year rate R0.\n        The yield volatility for period-3 is .\n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nBlack-Derman-Toy Model Developed by Team at Goldman Sachs\nA Binomial Interest Rate Model and the Black-Derman-Toy Model\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Risk-Neutral Valuation and Power Contractsis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Forwards is: <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. Here is the brief introduction of Forwards:\n        Latex code for the Forwards Contracts. I will briefly introduce the notations in this formulation. A forward contract is an agreement in which the buyer agrees at time t to pay the seller at time T and receive the asset at time T.\n        \n: Forward Contract at strike price S\n: Interest Rate\n: Future Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Forwards?"}
{"completion": " The related materials of Nominal Interest Rate is: 1.Merchandise imports:<url>https://data.worldbank.org/indicator/TM.VAL.MRCH.CD.WT</url>;", "tag": "Economics,MacroEconomics", "prompt": "Can you help me find related materials of Nominal Interest Rate?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion SDEs is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>U</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Optimal Combination of Resources Conditionis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Optimal Combination of Resources Condition?"}
{"completion": " The Latex Code for equation Socially Optimal Level of Outputis <equation>\\\\text{MSB} = \\\\text{MSC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Socially Optimal Level of Output?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A = Pe^{rt}</equation> in Compound Interest is: Loan/investment is compounded continuously.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>A = Pe^{rt}</equation> in Compound Interest?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I</equation> in Investment is: Investment.", "tag": "Economics,MacroEconomics", "prompt": "What is the meaning of the symbol <equation>I</equation> in Investment?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion is: Volatility.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>\\sigma</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The related materials of Future Value of Ordinary Annuities is: 1.Ordinary Annuity:<url>https://www.investopedia.com/terms/o/ordinaryannuity.asp</url>;", "tag": "Economics", "prompt": "Can you help me find related materials of Future Value of Ordinary Annuities?"}
{"completion": " The equation for Production Efficiency Condition is <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>. The meaning of symbol <equation>MP_{L}</equation> in Production Efficiency Condition is: Marginal Product Label.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MP_{L}</equation> in Production Efficiency Condition?"}
{"completion": " The Latex Code for equation Production Efficiency Conditionis <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Production Efficiency Condition?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is: <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. Here is the brief introduction of Cox-Ingersoll-Ross CIR:\n        Latex code for the Cox-Ingersoll-Ross model. \n        \n: 1-year interest rate.\n: 1-year bond price\n: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down.\n: Observed year-1 price of a 1-year bond\n\n\nRelated Documents\n\nCox-Ingersoll-Ross Model\nA THEORY OF THE TERM STRUCTURE OF INTEREST RATES\nCox-Ingersoll-Ross (CIR) model-Mathworks\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>S_{B}</equation> in Gini Coefficient is: Area of Triangle between X-axis (Cumulative of Families) and Y-axis(Cumulative of Income)..", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>S_{B}</equation> in Gini Coefficient?"}
{"completion": " The Latex Code for equation Tax Multiplieris <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Tax Multiplier?"}
{"completion": " The equation for Price for a Competitive Firm is <equation>P = MR</equation>. The meaning of symbol <equation>P</equation> in Price for a Competitive Firm is: Price.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>P</equation> in Price for a Competitive Firm?"}
{"completion": " The equation for Slope of the Total Product Curve is <equation>\\\\text{Marginal Product} = \\\\frac{\\\\Delta P}{\\\\Delta L} = \\\\frac{\\\\text{Rise}}{\\\\text{Run}} = \\\\frac{\\\\text{Change in Total Product}}{\\\\text{Change in the Number of Units of an Input}}</equation>. The meaning of symbol <equation>\\Delta Q</equation> in Slope of the Total Product Curve is: Change in Total Product.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta Q</equation> in Slope of the Total Product Curve?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>TP</equation> in Average Product is: Total Product.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>TP</equation> in Average Product?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Cox-Ingersoll-Ross CIR?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A = Pe^{rt}</equation> in Compound Interest is: Loan/investment is compounded continuously.", "tag": "Economics", "prompt": "What is the meaning of <equation>A = Pe^{rt}</equation> in Compound Interest?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>TC</equation> in Average Variable Cost is: Total Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>TC</equation> in Average Variable Cost?"}
{"completion": " The equation for Ito Lemma is <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. The meaning of symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma is: Stochastic differential equation for X(t).", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\mathrm{d}X(t)</equation> in Ito Lemma?"}
{"completion": " The equation for Ito Lemma is: <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>. Here is the brief introduction of Ito Lemma:\n        Latex code for the Ito Lemma.\n        \n: Diffusion\n: Stochastic differential equation for X(t)\n\n\nRelated Documents\n\nGeometric Brownian Motion\nGeometric Brownian motion\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Ito Lemma?"}
{"completion": " The Latex Code for equation Effective Rateis <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>", "tag": "Economics", "prompt": "Please give me some hints on equation Effective Rate?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e}</equation> in Effective Rate is: Effective Rate.", "tag": "Economics", "prompt": "What does the symbol mean <equation>r_{e}</equation> in Effective Rate?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e}</equation> in Effective Rate is: Effective Rate.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>r_{e}</equation> in Effective Rate?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(T)</equation> in Monte-Carlo Simulations is: The stock price at time T.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>S(T)</equation> in Monte-Carlo Simulations?"}
{"completion": " The Latex Code for equation Consumption Functionis <equation>C = C_{a} + \\\\text{MPC}(Y)</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Consumption Function?"}
{"completion": " The Latex Code for equation Unemployment Rateis <equation>\\\\text{Unemployment Rate} = \\\\frac{\\\\text{Unemployed}}{\\\\text{Labor Force}}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Unemployment Rate?"}
{"completion": " The Latex Code for equation Equation of Exchangeis <equation>\\\\text{MV} = \\\\text{PQ}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Equation of Exchange?"}
{"completion": " The related materials of Distributive Efficiency Condition is: 1.Distributive Efficiency Definition:<url>https://www.economicshelp.org/blog/glossary/distributive-efficiency/</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Distributive Efficiency Condition?"}
{"completion": " The equation for Sharpe Ratio is <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. The meaning of symbol <equation>\\delta</equation> in Sharpe Ratio is: Compounded Dividend Rate.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>\\delta</equation> in Sharpe Ratio?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor is: Change in Total Product(TP).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>\\Delta \\text{TP}</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Calls and Puts with Different Strikesis <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Calls and Puts with Different Strikes?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate is: Compute the effective rate if your loan/investment is compounded m times per year..", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>r_{e} = (1 + \\frac{r}{m})^{m} - 1</equation> in Effective Rate?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A</equation> in Compound Interest is: Future Value/Maturity Value.", "tag": "Economics", "prompt": "What is the meaning of the symbol <equation>A</equation> in Compound Interest?"}
{"completion": " The equation for Socially Optimal Level of Output is <equation>\\\\text{MSB} = \\\\text{MSC}</equation>. The meaning of symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output is: Marginal Social Cost.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>\\text{MSC}</equation> in Socially Optimal Level of Output?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>S(T)</equation> in Monte-Carlo Simulations is: The stock price at time T.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>S(T)</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t)</equation> in Standard Brownian Motion is: Value of Z at time stamp t.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Marginal Cost is <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost is: Change in Quantity.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\Delta \\text{Q}</equation> in Marginal Cost?"}
{"completion": " The Latex Code for equation Marginal Product of Laboris <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Marginal Product of Labor?"}
{"completion": " The equation for Investment is: <equation>I=I_{P}+I_{U}</equation>. Here is the brief introduction of Investment:\n        Latex code for the Investment. Investment during a period equals the sum of planned investment (I_P) and unplanned investment(I_U).\n        \n: Investment\n: Planned investment\n: Unplanned investment\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "What's the meaning of Investment?"}
{"completion": " The Latex Code for equation Bonds and Interest Ratesis <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Bonds and Interest Rates?"}
{"completion": " The equation for Optimal Consumption Rule is: <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. Here is the brief introduction of Optimal Consumption Rule:\n        Latex code for Optimal Consumption Rule. \n        \n: Marginal utility (MU)\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Optimal Consumption Rule?"}
{"completion": " The Latex Code for equation Price for a Competitive Firmis <equation>P = MR</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Price for a Competitive Firm?"}
{"completion": " The equation for Standard Brownian Motion is <equation>Z(t) \\\\sim N(0, t) \\\\\\\\\\ Z(t+s) - Z(t) \\\\sim N(0, s) \\\\\\\\\\ Z(t+s) \\\\sim N(Z(t), s)</equation>. The meaning of symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion is: Stationary increments of Standard Brownian Motion.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>Z(t+s) - Z(t)</equation> in Standard Brownian Motion?"}
{"completion": " The equation for Marginal Revenue Product of Labor MRPL is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL is: Marginal Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MP}_{L}</equation> in Marginal Revenue Product of Labor MRPL?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>ATC</equation> in Average Total Cost is: Average Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>ATC</equation> in Average Total Cost?"}
{"completion": " The Latex Code for equation Total Costsis <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Total Costs?"}
{"completion": " The Latex Code for equation Optimal Consumption Ruleis <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the latex code of equation Optimal Consumption Rule?"}
{"completion": " The Latex Code for equation Tax Multiplieris <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "What is the equation of Tax Multiplier?"}
{"completion": " The equation for Calls and Puts with Different Strikes is: <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. Here is the brief introduction of Calls and Puts with Different Strikes:\n\n        Latex code for the Calls and Puts with Different Strikes. For European calls and puts, with strike prices K_{1} and K_{2}, where K_{1} < K_{2}, we know the following.\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\n            American options, For three different options with strike prices K1 < K2 < K3:\n        \n\n: Call option of strike price K_{1}\n: Call option of strike price K_{2}\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "What's the meaning of Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Stock Prices as Geometric Brownian Motionis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>", "tag": "Financial,Economics", "prompt": "Show me the latex code of equation Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>P</equation> in Present Value of Ordinary Annuities is: Present Value.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>P</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Geometric Brownian Motion is <equation>Y(t) = Y(0)e^{X(t)} = Y(0)e^{[\\\\mu t + \\\\sigma Z(t)]} \\\\\\\\\\             E(e^{kU}) = e^{kE(U) + \\\\frac{1}{2}k^{2}\\\\text{Var}(U)} \\\\\\\\\\             E[Y^{k}(t)] = Y^{k}(0) e^{(k\\\\mu + \\\\frac{1}{2}k^{2}\\\\sigma^{2})t} \\\\\\\\\\             \\\\ln Y(t) \\\\sim N(\\\\ln Y(0) + \\\\mu t, \\\\sigma^{2} t)</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options is: Early Exercise getting the stock's dividend payments.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P_{V_{t},T}(dividends)</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Marginal Revenue Productis <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Marginal Revenue Product?"}
{"completion": " The equation for Calls and Puts with Different Strikes is <equation>K_{1} < K_{2} \\\\\\\\\\             0 \\\\le c(K_{1}) - c(K_{2}) \\\\le (K_{2} - K_{1})e^{-rT} \\\\\\\\\\             0 \\\\le p(K_{2}) - p(K_{1}) \\\\le (K_{2}) - K_{1})e^{-rT} \\\\\\\\\\             \\\\frac{c(K_{1}) - c(K_{2})}{K_{2} - K_{1}} \\\\ge \\\\frac{c(K_{2}) - c(K_{3})}{K_{3} - K_{2}} \\\\\\\\\\             \\\\frac{p(K_{1}) - p(K_{2})}{K_{2} - K_{1}} \\\\le \\\\frac{p(K_{3}) - p(K_{2})}{K_{3} - K_{2}}</equation>. The meaning of symbol <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes is: Call option of strike price K_{2}.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>c(K_{2})</equation> in Calls and Puts with Different Strikes?"}
{"completion": " The Latex Code for equation Factor of Production Hiring Ruleis <equation>\\\\text{MRP} = \\\\text{MFC}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Factor of Production Hiring Rule?"}
{"completion": " The related materials of Simple Interest is: 1.Investopedia Simple Interest:<url>https://www.investopedia.com/terms/s/simple_interest.asp</url>;", "tag": "Economics", "prompt": "Can you help me find related materials of Simple Interest?"}
{"completion": " The equation for Effective Rate is <equation>r_{e} = (1 + \\\\frac{r}{m})^{m} - 1 \\\\\\\\\\ r_{e} = e^{r} - 1</equation>. The meaning of symbol <equation>r_{e}</equation> in Effective Rate is: Effective Rate.", "tag": "Economics", "prompt": "What is the meaning of <equation>r_{e}</equation> in Effective Rate?"}
{"completion": " The Latex Code for equation Allocative Efficiency Conditionis <equation>P = MC \\\\\\\\\\ \\\\text{Marginal Social Benefit (MSB)} = \\\\text{Marginal Social Cost (MSC)}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Allocative Efficiency Condition?"}
{"completion": " The equation for Real GDP is: <equation>\\\\text{Real GDP}=\\\\frac{Nominal GDP}{CPI for the same year as the nominal figure} \\\\times 100</equation>. Here is the brief introduction of Real GDP:\n        Latex code for Real GDP.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Real GDP?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates is: Non-continuous annualized rate.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Nominal Interest Rate is: <equation>\\\\text{Nominal Interest Rate}=\\\\text{Real Interest Rate} + \\\\text{Anticipated Inflation}</equation>. Here is the brief introduction of Nominal Interest Rate:\n        Latex code for Nominal Interest Rate.\n        \n \n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Nominal Interest Rate?"}
{"completion": " The equation for Profit is <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. The meaning of symbol <equation>\\text{TC}</equation> in Profit is: Total Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{TC}</equation> in Profit?"}
{"completion": " The Latex Code for equation Gini Coefficientis <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Gini Coefficient?"}
{"completion": " The equation for Autonomous Spending Multiplier is: <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>. Here is the brief introduction of Autonomous Spending Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n: Marginal Propensity Save\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Autonomous Spending Multiplier?"}
{"completion": " The equation for Average Total Cost is <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Total Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>Q</equation> in Average Total Cost?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates is: Non-continuous annualized rate.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Bonds and Interest Ratesis <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Bonds and Interest Rates?"}
{"completion": " The Latex Code for equation Ito Lemmais <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Ito Lemma?"}
{"completion": " The equation for Average Product is <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. The meaning of symbol <equation>TP</equation> in Average Product is: Total Product.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>TP</equation> in Average Product?"}
{"completion": " The equation for Optimal Consumption Rule is <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. The meaning of symbol <equation>P</equation> in Optimal Consumption Rule is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P</equation> in Optimal Consumption Rule?"}
{"completion": " The equation for Optimal Consumption Rule is: <equation>\\\\frac{MU_{x}}{P_{x}} = \\\\frac{MU_{Y}}{P_{Y}}</equation>. Here is the brief introduction of Optimal Consumption Rule:\n        Latex code for Optimal Consumption Rule. \n        \n: Marginal utility (MU)\n: Price\n\n\nRelated Documents\n\nHow Is the Marginal Product of Labor Determined\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Optimal Consumption Rule?"}
{"completion": " The equation for Gini Coefficient is <equation>G = \\\\frac{S_{A}}{S_{B}} \\\\\\\\\\ G = 1 - \\\\sum^{n}_{i=1} P_{i} \\\\times (2 Q_{i} - W_{i}) \\\\\\\\\\ Q_{i} = \\\\sum^{i}_{k = 1} W_{k}</equation>. The meaning of symbol <equation>Q_{i}</equation> in Gini Coefficient is: The ratio of cumulative i-th group's income(increasing order)/total income.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>Q_{i}</equation> in Gini Coefficient?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: American Call Option Price.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>C(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Annuities Due is <equation>S = R \\\\times \\\\frac{(1+i)^(n+1) - 1}{i} - R</equation>. The meaning of symbol <equation>S</equation> in Annuities Due is: Future Value/Total amount accrued.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>S</equation> in Annuities Due?"}
{"completion": " The equation for Black-Derman-Toy BDT is <equation>\\\\text{First Node: 1-year bond price} \\\\\\\\\\             P_{0} = \\\\frac{1}{1 + R_{0}} \\\\\\\\\\             \\\\text{Second Node} \\\\\\\\\\             P_{1} = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2} P(1,2,r_{u}) + \\\\frac{1}{2} P(1,2,r_{d})] \\\\\\\\\\             = \\\\frac{1}{1+R_{0}} [\\\\frac{1}{2(1 + R_{1}e^{2\\\\sigma_{1}})} + \\\\frac{1}{2(1 + R_{1})}] \\\\\\\\\\             R_{0} = \\\\frac{1}{2} \\\\ln (\\\\frac{R_{1} e^{2\\\\sigma_{1}} }{R_{1}})</equation>. The meaning of symbol <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT is: year-1 price of a 1-year bond, depending on the movement of the interest rate moving up and down..", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P(1, 2, r_{u}), P(1, 2, r_{d})</equation> in Black-Derman-Toy BDT?"}
{"completion": " The Latex Code for equation Price Elasticity of Demandis <equation>\\\\text{Price Elasticity of Demand} = \\\\frac{% \\\\Delta Q_{d}}{% \\\\Delta P} = \\\\frac{\\\\frac{\\\\Delta Q_{d}}{Q}}{\\\\frac{\\\\Delta P}{P}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Price Elasticity of Demand?"}
{"completion": " The Latex Code for equation Distributive Efficiency Conditionis <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Distributive Efficiency Condition?"}
{"completion": " The equation for Sharpe Ratio is: <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>. Here is the brief introduction of Sharpe Ratio:\n        Latex code for Sharpe Ratio.\n        \n: Compounded Dividend Rate\n: Sharpe ratio\n: Sharpe ratio of any asset written on a GBM\n\n\nRelated Documents\n\nSharpe Ratio Formula and Definition With Examples\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "I am interested in Sharpe Ratio?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>t</equation> in Compound Interest is: Time (years).", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>t</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Factor of Production Hiring Ruleis <equation>\\\\text{MRP} = \\\\text{MFC}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Factor of Production Hiring Rule?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion is: Drift coefficient.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>\\mu</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition is: Marginal Utility of C.", "tag": "Economics,Microeconomics", "prompt": "Can you explain the symbol <equation>MU_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Balanced Budget Multiplier is <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. The meaning of symbol <equation>MPC</equation> in Balanced Budget Multiplier is: Marginal Propensity to Consume.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>MPC</equation> in Balanced Budget Multiplier?"}
{"completion": " The equation for Profit-Maximizing Output Level is <equation>MR = MC</equation>. The meaning of symbol <equation>\\text{MR}</equation> in Profit-Maximizing Output Level is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MR}</equation> in Profit-Maximizing Output Level?"}
{"completion": " The equation for Tax Multiplier is: <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>. Here is the brief introduction of Tax Multiplier:\n        Latex code for Tax Multiplier.\n        \n\n\nRelated Documents\n\nMerchandise imports\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Tax Multiplier?"}
{"completion": " The Latex Code for equation Marginal Factor Cost MFCis <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Marginal Factor Cost MFC?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>i</equation> in Present Value of Ordinary Annuities is: Rate per period, usually i=r/m.", "tag": "Economics", "prompt": "Can you explain the symbol <equation>i</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Consumer Price Index CPI is: <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Consumer Price Index CPI:\n        Latex code for Consumer Price Index CPI.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you explain Consumer Price Index CPI?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{C}</equation> in Distributive Efficiency Condition is: Product of C.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P_{C}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MP</equation> in Marginal Revenue Product is: Marginal Product(MP).", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MP</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>P</equation> in Compound Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "What is the meaning of <equation>P</equation> in Compound Interest?"}
{"completion": " The Latex Code for equation Early Exercise for American Optionsis <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>", "tag": "Financial,Economics", "prompt": "What is the latex code of equation Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Future Value of Ordinary Annuitiesis <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>", "tag": "Economics", "prompt": "What is the equation of Future Value of Ordinary Annuities?"}
{"completion": " The Latex Code for equation Real Interest Rateis <equation>\\\\text{Real Interest Rate} = \\\\text{Nominal Interest Rate} \u2013 \\\\text{Anticipated Inflation}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Real Interest Rate?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>P_{F}</equation> in Distributive Efficiency Condition is: Product of F.", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>P_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The equation for Total Costs is: <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. Here is the brief introduction of Total Costs:\n        Latex code for Socially Optimal Level of Output.\n        \n: Total Costs (TC)\n: Total Fixed Costs (TFC)\n: Total Variable Costs (TVC)\n\n\nRelated Documents\n\nTotal Variable Costs\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Total Costs?"}
{"completion": " The equation for Forwards is <equation>F_{t,T}(S) = S_{t}e^{r(T-t)} = S_{t}e^{r(T-t)} - FV_{t,T}(\\\\text{Dividends}) = S_{t}e^{(r-\\\\delta)(T-t)}</equation>. The meaning of symbol <equation>r</equation> in Forwards is: Interest Rate.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>r</equation> in Forwards?"}
{"completion": " The Latex Code for equation Future Value of Ordinary Annuitiesis <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>", "tag": "Economics", "prompt": "Can you write equation Future Value of Ordinary Annuities?"}
{"completion": " The equation for Equality of Leakages and Injections is: <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>. Here is the brief introduction of Equality of Leakages and Injections:\n        Latex code for Equality of Leakages and Injections. Injection and leakages in economics, Some transactions put money into the economy \u00e2\u20ac\u201c that is, the money is being utilised elsewhere in the economy. These are injections. Some transactions take money out of the economy. That is, the money is not being utilised elsewhere in the economy. These are leakages.\n        \n: Investment\n: Government Spending\n: Exports\n\n\nRelated Documents\n\nWhy are leakages equal to injections?\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "I am interested in Equality of Leakages and Injections?"}
{"completion": " The equation for Monte-Carlo Simulations is <equation>S(T) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})T + \\\\sigma \\\\sqrt{T} z} \\\\\\\\\\             S(T) = S(t) e^{(a - \\\\delta - \\\\frac{\\\\sigma^2}{2})(T-t) + \\\\sigma (Z(T) - Z(t))} \\\\\\\\\\             \\\\text{Variance} \\\\\\\\\\             e^{-2rT} \\\\times \\\\frac{s^{2}}{n} \\\\\\\\\\             s^{2} = \\\\frac{1}{n-1} \\\\sum [(g(S_{i}) - \\\\bar{g})]^{2}</equation>. The meaning of symbol <equation>g_{i}</equation> in Monte-Carlo Simulations is: The i-th simulated payoff.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>g_{i}</equation> in Monte-Carlo Simulations?"}
{"completion": " The equation for Investment is <equation>I=I_{P}+I_{U}</equation>. The meaning of symbol <equation>I_{P}</equation> in Investment is: Planned investment.", "tag": "Economics,MacroEconomics", "prompt": "Help me find the meaning of symbol <equation>I_{P}</equation> in Investment?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>Q</equation> in Average Variable Cost is: Quantity of Output.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>Q</equation> in Average Variable Cost?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The related materials of Effective Rate is: 1.Investopedia Effective Rate:<url>https://www.investopedia.com/terms/e/effectiveinterest.asp</url>;", "tag": "Economics", "prompt": "Can you help me find related materials of Effective Rate?"}
{"completion": " The Latex Code for equation Marginal Costis <equation>\\\\text{MC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{Q}} = \\\\frac{\\\\Delta \\\\text{TVC}}{\\\\Delta \\\\text{Q}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Show me the latex code of equation Marginal Cost?"}
{"completion": " The equation for Stock Prices as Geometric Brownian Motion is <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (a - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             S(t) = S(0) e^{(a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2})t + \\\\sigma Z(t)} \\\\\\\\\\             \\\\mathrm{d}[\\\\ln S(t)] = (a - \\\\delta - \\\\frac{\\\\sigma^{2}}{2}) \\\\mathrm{d}t + \\\\sigma \\\\sigma \\\\mathrm{d} Z(t) \\\\\\\\\\             S(t) \\\\sim \\\\ln( \\\\ln S(0) + (a - \\\\delta - \\\\frac{\\\\sigma^2}{2})t, \\\\sigma^{2}t)</equation>. The meaning of symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>U</equation> in Stock Prices as Geometric Brownian Motion?"}
{"completion": " The equation for Balanced Budget Multiplier is: <equation>\\\\text{Balanced Budget Multiplier} = \\\\frac{1}{1-MPC} +  \\\\frac{-MPC}{1-MPC}  = 1</equation>. Here is the brief introduction of Balanced Budget Multiplier:\n        Latex code for the Autonomous Spending Multiplier.\n        \n: Marginal Propensity to Consume\n\n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Balanced Budget Multiplier?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TVC}</equation> in Total Costs is: Total Variable Costs (TVC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{TVC}</equation> in Total Costs?"}
{"completion": " The Latex Code for equation Ito Lemmais <equation>\\\\mathrm{d}X(t) = a(t, X(t)) \\\\mathrm{d}t + b(t, X(t))\\\\mathrm{d} Z(t) \\\\\\\\\\             Y(t) = f(t, X(t)) \\\\mathrm{d}t \\\\\\\\\\             \\\\mathrm{d} Y(t) = f_{t}(t, X(t)) + f_{x}(t, X(t))\\\\mathrm{d} X(t) + \\\\frac{1}{2} f_{xx}(t, X(t))[\\\\mathrm{d}X(t)]^{2} \\\\\\\\\\             [\\\\mathrm{d} X(t)]^{2} = b^{2}(t, X(t))\\\\mathrm{d} t</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Ito Lemma?"}
{"completion": " The equation for Call and Put Price Bounds is: <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. Here is the brief introduction of Call and Put Price Bounds:\n\n        Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.\n        \n\n: European Call Option Price\n: European Put Option Price\n: American Call Option Price\n: American Put Option Price\n\n\nRelated Documents\n\nInvestopedia Put Call Parity\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Call and Put Price Bounds?"}
{"completion": " The equation for Banks Reserve Ratio is: <equation>\\\\text{Reserve Ratio} = \\\\frac{\\\\text{Bank Reserves}}{\\\\text{Total Deposits}}</equation>. Here is the brief introduction of Banks Reserve Ratio:\n        Latex code for the Banks Reserve Ratio.\n        \n \n\nRelated Documents\n\nPrinciples Economics\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Can you give me a brief introduction to Banks Reserve Ratio?"}
{"completion": " The Latex Code for equation Autonomous Spending Multiplieris <equation>\\\\text{Multiplier} = \\\\frac{1}{1-MPC} = \\\\frac{1}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Show me the latex code of equation Autonomous Spending Multiplier?"}
{"completion": " The Latex Code for equation Optimal Combination of Resources Conditionis <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>", "tag": "Economics,Microeconomics", "prompt": "Please give me some hints on equation Optimal Combination of Resources Condition?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>n</equation> in Future Value of Ordinary Annuities is: Total number of times compounded.", "tag": "Economics", "prompt": "What is the meaning of <equation>n</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Bonds and Interest Rates is: <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. Here is the brief introduction of Bonds and Interest Rates:\n        Latex code for the Bonds and Interest Rates. The price of an s-year zero is P(0, S). The forward bond price formula  is calculated as . And the \n        non-continuous annualized rate is .\n        \n: Price of an s-year zero.\n: Forward Bond Price\n: Non-continuous annualized rate\n\n\nRelated Documents\n\nBond and Interest Rate\nUnderstanding Interest Rates, Inflation, and Bonds\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Bonds and Interest Rates?"}
{"completion": " The equation for Marginal Product of Labor is <equation>\\\\text{MPL} = \\\\frac{\\\\Delta \\\\text{TP}}{\\\\Delta \\\\text{L}}</equation>. The meaning of symbol <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor is: Change in Labor(L).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\Delta \\text{L}</equation> in Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Production Efficiency Conditionis <equation>\\\\frac{w}{r} = \\\\frac{MP_{L}}{MP_{K}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Production Efficiency Condition?"}
{"completion": " The equation for Marginal Factor Cost MFC is <equation>\\\\text{MFC} = \\\\frac{\\\\Delta \\\\text{TC}}{\\\\Delta \\\\text{f}}</equation>. The meaning of symbol <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC is: Marginal Factor Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>\\text{MFC}</equation> in Marginal Factor Cost MFC?"}
{"completion": " The related materials of Marginal Product of Labor is: 1.How Is the Marginal Product of Labor Determined:<url>https://www.masterclass.com/articles/learn-about-marginal-product-of-labor-in-economics</url>;", "tag": "Economics,Microeconomics", "prompt": "Can you help me find related materials of Marginal Product of Labor?"}
{"completion": " The Latex Code for equation Average Variable Costis <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Average Variable Cost?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue Product is: Marginal Revenue(MR).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MR</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Present Value of Ordinary Annuities is <equation>P = R \\\\frac{1 - (1+r)^{-n}}{i} \\\\\\\\\\ R = P \\\\frac{i}{1 - (1+r)^{-n}}</equation>. The meaning of symbol <equation>P</equation> in Present Value of Ordinary Annuities is: Present Value.", "tag": "Economics", "prompt": "What does the symbol mean <equation>P</equation> in Present Value of Ordinary Annuities?"}
{"completion": " The equation for Total Costs is <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>. The meaning of symbol <equation>\\text{TFC}</equation> in Total Costs is: Total Fixed Costs (TFC).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{TFC}</equation> in Total Costs?"}
{"completion": " The equation for Factor of Production Hiring Rule is: <equation>\\\\text{MRP} = \\\\text{MFC}</equation>. Here is the brief introduction of Factor of Production Hiring Rule:\n        Latex code for Factor of Production Hiring Rule. I will briefly introduce the notations in this formulation.  \n        \n: Marginal revenue product\n: Marginal factor cost (MFC)\n\n\nRelated Documents\n\nThe Demand for Labor\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "What's the meaning of Factor of Production Hiring Rule?"}
{"completion": " The equation for Consumer Price Index CPI is: <equation>\\\\text{CPI} = \\\\frac{\\\\text{Base Year Quantities} \\\\times \\\\text{Current Year Prices}}{\\\\text{Base Year Quantities} \\\\times \\\\text{Base Year Prices}} \\\\times 100</equation>. Here is the brief introduction of Consumer Price Index CPI:\n        Latex code for Consumer Price Index CPI.\n        \n \n\nRelated Documents\n\nCPI Home : U.S. Bureau of Labor Statistics\nInvestopedia: Consumer Price Index\n\nRelated Videos\n\n\n", "tag": "Economics,MacroEconomics", "prompt": "Please give me detailed tutorial of Consumer Price Index CPI?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MP</equation> in Marginal Revenue Product is: Marginal Product(MP).", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>MP</equation> in Marginal Revenue Product?"}
{"completion": " The Latex Code for equation Total Costsis <equation>\\\\text{TC} = \\\\text{TFC} + \\\\text{TVC}</equation>", "tag": "Economics,Microeconomics", "prompt": "What is the equation of Total Costs?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Call Option Price.", "tag": "Financial,Economics", "prompt": "Help me find the meaning of symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The equation for Call and Put Price Bounds is <equation>(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \\\\le c(S_{t},K,t,T) \\\\le F^{P}_{t,T}(S) \\\\\\\\\\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \\\\le p(S_{t},K,t,T) \\\\le Ke^{-r(T-t)} \\\\\\\\ c(S_{t},K,t,T) \\\\le C(S_{t},K,t,T) \\\\le S_{t} \\\\\\\\\\ p(S_{t},K,t,T) \\\\le P(S_{t},K,t,T) \\\\le K</equation>. The meaning of symbol <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds is: European Call Option Price.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>c(S_{t},K,t,T)</equation> in Call and Put Price Bounds?"}
{"completion": " The related materials of Geometric Brownian Motion is: 1.Geometric Brownian Motion:<url>https://www.quantstart.com/articles/Geometric-Brownian-Motion/</url>;2.Geometric Brownian motion:<url>http://www.columbia.edu/~ks20/FE-Notes/4700-07-Notes-GBM.pdf</url>;", "tag": "Financial,Economics", "prompt": "Can you help me find related materials of Geometric Brownian Motion?"}
{"completion": " The Latex Code for equation Average Total Costis <equation>\\\\text{Average Total Cost(ATC)} = \\\\frac{\\\\text{Total Cost (TC)}}{\\\\text{Quantity of Output (Q)}}</equation>", "tag": "Economics,Microeconomics", "prompt": "Can you write equation Average Total Cost?"}
{"completion": " The equation for Profit is: <equation>\\\\text{Profit} = \\\\text{TR} \u2013 \\\\text{TC}</equation>. Here is the brief introduction of Profit:\n        Latex code for Price for a Competitive Firm.\n        \n: Total Revenue\n: Total Cost\n\n\nRelated Documents\n\nProfit\n\nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you give me a brief introduction to Profit?"}
{"completion": " The equation for Average Variable Cost is <equation>\\\\text{Average Variable Cost(AVC)} = \\\\frac{\\\\text{Total Variable Cost (TVC)}}{\\\\text{Quantity of Output (Q)}}</equation>. The meaning of symbol <equation>AVC</equation> in Average Variable Cost is: Average Variable Cost.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>AVC</equation> in Average Variable Cost?"}
{"completion": " The Latex Code for equation Geometric Brownian Motion SDEsis <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>", "tag": "Financial,Economics", "prompt": "Can you write equation Geometric Brownian Motion SDEs?"}
{"completion": " The Latex Code for equation Tax Multiplieris <equation>\\\\text{Tax Multiplier} = -\\\\frac{MPC}{MPS}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Can you write equation Tax Multiplier?"}
{"completion": " The equation for Distributive Efficiency Condition is <equation>\\\\frac{MU_{F}}{P_{F}} = \\\\frac{MU_{C}}{P_{C}}</equation>. The meaning of symbol <equation>MU_{F}</equation> in Distributive Efficiency Condition is: Marginal Utility of F.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>MU_{F}</equation> in Distributive Efficiency Condition?"}
{"completion": " The Latex Code for equation Sharpe Ratiois <equation>\\\\frac{\\\\mathrm{d}X(t)}{X(t)} = m \\\\mathrm{d}t + s \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\phi = \\\\frac{m + \\\\delta -r }{s} \\\\\\\\\\             \\\\phi = \\\\frac{a - r}{\\\\sigma}</equation>", "tag": "Financial,Economics", "prompt": "How to write equation Sharpe Ratio?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>Y(t)</equation> in Geometric Brownian Motion SDEs is: Observed value Y(t) at time stamp t.", "tag": "Financial,Economics", "prompt": "What is the meaning of <equation>Y(t)</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>A = Pe^{rt}</equation> in Compound Interest is: Loan/investment is compounded continuously.", "tag": "Economics", "prompt": "Help me find the meaning of symbol <equation>A = Pe^{rt}</equation> in Compound Interest?"}
{"completion": " The equation for Geometric Brownian Motion SDEs is <equation>\\\\mathrm{d}Y(t) = \\\\mu Y(t)dt + \\\\sigma Y(t) \\\\mathrm{d}Z(t) \\\\\\\\\\             \\\\mathrm{d}[\\\\ln Y(t)] = (\\\\mu - \\\\frac{\\\\sigma^2}{2}) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d}Z(t) \\\\\\\\\\             Y(t) = T(0) e^{(\\\\mu - \\\\frac{\\\\sigma^2}{2})t + \\\\sigma Z(t)}</equation>. The meaning of symbol <equation>U</equation> in Geometric Brownian Motion SDEs is: Any normal random variable.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>U</equation> in Geometric Brownian Motion SDEs?"}
{"completion": " The equation for Compound Interest is <equation>A = P(1+\\\\frac{r}{m})^{mt} \\\\\\\\\\ A = Pe^{rt}</equation>. The meaning of symbol <equation>P</equation> in Compound Interest is: Principal/Present Value.", "tag": "Economics", "prompt": "What does the symbol mean <equation>P</equation> in Compound Interest?"}
{"completion": " The equation for Asian Options is: <equation>A(T) = \\\\frac{1}{n} \\\\sum S(ih) \\\\\\\\\\ G(T) = [\\\\prod S(ih)]^{\\\\frac{1}{n}}</equation>. Here is the brief introduction of Asian Options:\n        Latex code for the Asian options are options. Asian options are options that are based on averages in place of either the price or the strike. The average can be either an arithmetic average or a geometric average. Then to price the option replace either the strike or the price with the appropriate path-dependent average, calculate the payoffs, and then discount them.\n        \n: Arithmetic average of option price at time T\n: Geometric average of option price at time T\n\n\nRelated Documents\n\nWhat Is an Asian Option? How They Work Vs. Standard Options\n\nRelated Videos\n\n\n", "tag": "Financial,Economics", "prompt": "Can you give me a brief introduction to Asian Options?"}
{"completion": " The equation for Marginal Revenue Product is <equation>\\\\text{MRP} = \\\\text{MP} \\\\times \\\\text{MR}</equation>. The meaning of symbol <equation>MP</equation> in Marginal Revenue Product is: Marginal Product(MP).", "tag": "Economics,Microeconomics", "prompt": "What does the symbol mean <equation>MP</equation> in Marginal Revenue Product?"}
{"completion": " The equation for Marginal Revenue is <equation>\\\\text{MR} = \\\\frac{\\\\Delta \\\\text{TR}}{\\\\Delta \\\\text{Q}}</equation>. The meaning of symbol <equation>MR</equation> in Marginal Revenue is: Marginal Revenue.", "tag": "Economics,Microeconomics", "prompt": "Help me find the meaning of symbol <equation>MR</equation> in Marginal Revenue?"}
{"completion": " The equation for Average Product is: <equation>\\\\text{AP} = \\\\frac{\\\\text{Total Product}}{\\\\text{Quantity of Input}}</equation>. Here is the brief introduction of Average Product:\n        Latex code for the Average Product. I will briefly introduce the notations in this formulation.  \n        \n: Average Product\n: Total Product\n: Quantity of Input\n\n\nRelated Documents\n\n \nRelated Videos\n\n\n", "tag": "Economics,Microeconomics", "prompt": "Can you explain Average Product?"}
{"completion": " The Latex Code for equation Average Fixed Costis <equation>AFC = \\\\frac{Total Fixed Cost (TFC)}{Quantity of Output (Q)}</equation>", "tag": "Economics,Microeconomics", "prompt": "How to write equation Average Fixed Cost?"}
{"completion": " The Latex Code for equation Risk-Neutral Valuation and Power Contractsis <equation>\\\\frac{\\\\mathrm{d}S(t)}{S(t)} = (r - \\\\delta) \\\\mathrm{d}t + \\\\sigma \\\\mathrm{d} \\\\tilt{Z}(t) \\\\\\\\\\             \\\\tilt{Z}(t) = Z(t) + \\\\phi t \\\\\\\\\\             V(S(t), t) = e^{-r(T-t)} E^{*}[V(S(T), T) | S(T)] \\\\\\\\\\             F^{p}_{t, T}(S^{a}) = S^{a}(t) e ^{ (-r + a(r-\\\\delta) + \\\\frac{1}{2} a(a-1)\\\\sigma^{2})(T-t)}</equation>", "tag": "Financial,Economics", "prompt": "Please give me some hints on equation Risk-Neutral Valuation and Power Contracts?"}
{"completion": " The equation for Calls and Puts Arbitrage is <equation>K_{1} < K_{2} < K_{3} \\\\\\\\\\ K_{2} = \\\\lambda K_{1} + (1 - \\\\lambda) K_{3} \\\\\\\\\\ \\\\lambda = \\\\frac{K_{3} - K_{2}}{K_{3} - K_{1}}</equation>. The meaning of symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage is: Strike price of option 3.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>K_{3}</equation> in Calls and Puts Arbitrage?"}
{"completion": " The equation for Future Value of Ordinary Annuities is <equation>S = R \\\\times \\\\frac{(1+i)^n - 1}{i} \\\\\\\\\\ R = S \\\\times \\\\frac{i}{(1+i)^n - 1}</equation>. The meaning of symbol <equation>R</equation> in Future Value of Ordinary Annuities is: Payment/Deposit made in each period.", "tag": "Economics", "prompt": "What is the meaning of <equation>R</equation> in Future Value of Ordinary Annuities?"}
{"completion": " The equation for Early Exercise for American Options is <equation>P_{V_{t},T}(dividends) > p(S_{t}, K) + K(1 ? e^{?r(T ?t)}) \\\\\\\\\\ K(1 ? e^{?r(T ?t)}) > c(S_{t}, K) + P_{V_{t},T}(dividends)</equation>. The meaning of symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options is: put protection if the stock price should fall..", "tag": "Financial,Economics", "prompt": "Can you explain the symbol <equation>p(S_{t}, K)</equation> in Early Exercise for American Options?"}
{"completion": " The Latex Code for equation Equality of Leakages and Injectionsis <equation>\\\\text{S} + \\\\text{T} + \\\\text{M} = \\\\text{I} + \\\\text{G} + \\\\text{X}</equation>", "tag": "Economics,MacroEconomics", "prompt": "Please give me some hints on equation Equality of Leakages and Injections?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>P</equation> in Optimal Combination of Resources Condition is: Price.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of <equation>P</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Simple Interest is: <equation>I=Prt \\\\\\\\\\ A=P(1+rt)</equation>. Here is the brief introduction of Simple Interest:\n        Latex code for the Simple Interest. I will briefly introduce the notations in this formulation. \n        \n: Interest Earned\n: Principal/Present Value\n: Annual Rate\n: Time (years)\n: Future Value/Maturity Value\n\n\nRelated Documents\n\nInvestopedia Simple Interest\n\nRelated Videos\n\n\n", "tag": "Economics", "prompt": "I am interested in Simple Interest?"}
{"completion": " The equation for Optimal Combination of Resources Condition is <equation>\\\\text{MRP}_{L} = \\\\text{MP}_{L} \\\\times \\\\text{P}</equation>. The meaning of symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition is: Marginal Revenue Product of Labor.", "tag": "Economics,Microeconomics", "prompt": "What is the meaning of the symbol <equation>\\text{MRP}_{L}</equation> in Optimal Combination of Resources Condition?"}
{"completion": " The equation for Bonds and Interest Rates is <equation>P(0, S) = \\\\frac{1}{[1 + r(0, s)]^{s}} \\\\text{or} e^{-r(0,s)s} \\\\\\\\\\ \\\\text{Forward bond price} \\\\\\\\\\ F_{t,T}[P(T, T+s)] = \\\\frac{P(t, T+s)}{P(t, T)} \\\\\\\\\\ P(t, T)[1 + r_{t}(T, T+s)]^{-s} = P(t, T+s)</equation>. The meaning of symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates is: Non-continuous annualized rate.", "tag": "Financial,Economics", "prompt": "What is the meaning of the symbol <equation>P(t, T)[1 + r_{t}(T, T+s)]^{-s}=P(t,T+s)</equation> in Bonds and Interest Rates?"}
{"completion": " The equation for Cox-Ingersoll-Ross CIR is <equation>\\\\mathrm{d} r(t) = a[b - r(t)]  \\\\mathrm{d} t + \\\\sigma \\\\sqrt{r(t)} \\\\mathrm{d} Z(t) \\\\\\\\\\             P(r, t, T) = A(T-t)e^{-rB(T-t)} \\\\\\\\\\             \\\\gamma = \\\\sqrt{(a-\\\\bar{\\\\phi})^{2} + 2 \\\\sigma^{2}} \\\\\\\\\\             q(r, t, T) = \\\\sigma \\\\sqrt{r} B(T-t) \\\\\\\\\\             \\\\text{yield to maturity} \\\\\\\\\\             \\\\frac{2ab}{ a - \\\\bar{\\\\phi} + \\\\gamma}</equation>. The meaning of symbol <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR is: 1-year bond price.", "tag": "Financial,Economics", "prompt": "What does the symbol mean <equation>P_{0}</equation> in Cox-Ingersoll-Ross CIR?"}